document resume ir 003 195 - eric · colloid and surface chemistry 23 computer languages 32 digital...

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IR 003 195

16mm Film and Videotape'Lectures and Demonstrations.1976/1977 COalog.Massachusetts Inst. of Tech., Cambridge. Center forAdvanced Engineering Study.76101p.Massachusetts Institute of Technology, Center forAdvanced Engineering Study, Cambridge, Massachusetts02139

EDRS PRICE MF-$0.83 HC -$6.O1 Plus PostageDESCRIPTORS Artificial Intelligence; Calculus; *Catalogs;

Chemistry; Computer Science; Economics; Electronics;Engineering; Experiments; Higher Education;*Instructional Films; Mathematics; Physics;Probability Theory; *Sciences; Statistics; SystemsAnalysis; Thermodynamics; *Video Tape Recordings

IDENTIFIERS Massachusetts Institute of Technology

ABSTEACTThe Massachusetts Institute of Technology provides a

catalog of 16mm filmed and videotaped lectures and demonstrations.Each listing includes title, short description, length ofpresentation, catalog number, purchase and rental prices, andindications as to whether the item is film or videotape andblack-and-white or color. The catalog is divided into 17 categories:artificial intelligence; calculus; colloid and surface chemistry;computer languages; digital signal processing; economics; engineeringeconomy; friction, wear, and lubrication; introduction toexperimentation; mechanics of polymer processing; modern controltheory; network analysis and design; nonlinear vibrations;probability; random processes; thermostatics and thermodynamics; andspecial programs. Ordering information and forms are included.(LS)

************************************************************************ Documents acquired by ERIC include many informal unpublished* materials not available from other sources. ERIC makes every effort ** to obtain the best copy available. Nevertheless, items of marginal *

* reproducibility are often encountered and this affects the quality *

* of the microfiche and hardcopy reproductions ERIC makes available *

* via the ERIC Document Reproduction Service (URS). EDRS is not* responsible for the quality of the original document. Reproductions ** supplied by EDRS are the best that can be made from the original.***********************************************************************

MassachusettsInstitute ofTechnology 16mm Film and

VideotapeLectures andDemonstrations

1976/1977Catalog

U.S. DEPARTMENT OF HEALTH,EDUCATION & WELFARENATIONAL INSTITUTE OF

EDUCATION

THIS DOCUMENT HAS BEEN REPRO-DUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGIN.ATING IT POINTS OF VIEW OR OPINIONSSTATED DO NOT NECESSARILY REPRESENT OFFICIAL NATIONAL INSTITUTE OFEDUCATION POSITION OR POLICY

The Massachusetts. Institute ofTechnology has developed morethan 450 videotapes and 16 mmfilms on the sciences, mathemat-ics, engineering, and management.

Produced at the Center forAdvanced Engineering Study incooperation with MIT and otherfaculty members, these programswere created as part of a self-study project for practicingengineers, industrial scientists,and technical managers.

Flexibly designed to meet indi-vidual learner needs, theselectures and demonstrations willbe useful to industry and on-campus graduate and undergraduateclasses.

Detailed study guides, includinglecture notes, reading assign-ments, problem sets, and solutionsaccompany most of the subjects.

Descriptions of the filmsand videotapes follow. Pleasenote the substantial discountsfor complete set rental orpurchase. Reservation formsare included to facilitate yourordering.

Artificial Intelligence 2

Calculus 6

Colloid and Surface Chemistry 23

Computer Languages 32

Digital Signal Processing 37

Economics 41

Engineering Economy 45

Friction, Wear, and Lubrication 48

Introduction to Experimentation 51

Mechanics of Polymer Processing 54

Modern Control Theory 60.

Network Analysis and Design 70

Nonlinear Vibrations 74

Probability ,78

Random Processes 86

Thermostatics and Thermodynamics' 93

Special Programs 96

I

Artificial IntelligencePatrick H. Winston

Artificial Intelligence is the-science of making computers smart.It is practiced both by those whowant to make computers moreuseful and by those who want tounderstand the nature of intel-ligence.

Intelligent systems will be betterbecause they will know why some-thing is wanted as well as whatis wanted. But, making machinessmart is also a new kind of psy-chology. Artificial Intelligence

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researchers believe that intelli-gence is the product of a familyOf qualities that can be studiedabstractly and without concernfor the particular hardware or"brainware" machines that manifestintelligence.

Patrick H. Winston is AssociateProfessor of Computer Science atMIT and Director of the MIT Arti-ficial Intelligence Laboratory.

Nr

Artificial IntelligenceTwenty-fourColor Videotapes

Geometric Analogy Problems (1)Purposeful descriptions.Symbolic pattern matching.Descriptions of relations andtransformations. Rule comparison.

26-min. Color Videotape17-0101 Purchase $245 Rental $25.

Geometric Analogy Problems (2)Geometric analogy examples. Re-marks on improving performance.The role of analogy in identify-ing unknown objects.


The General Problem SolverUsing goals and subgoals. Dif-ference descriptions, operators,and conditions. Iteration, ee-cursion, and automatic backup.Traveling to Aunt Agatha's.


Solving Calculus Problems (1)Goal trees and heuristic search.Judging difficulty and focusingattention. Strong and weaktransformations.


Solving Calculus Problems (2)Alternatives in performancemeasurement. Depth-first,breadth-first, and environment-driven search. Using programs asmetaphors. The ephemeral qualityof intelligence.


Perceptrons and Hill ClimbingThe perceptron idea. The in-ability of perceptrons to recog-nize connectivity. Learningthrough parameter twiddling.Foothill, ridge, and plateauproblems. The need for layers ofinformation processing.

34-min. Color Videotape17-0106 Purchase $300 Rental $30..

Picking The Next MoveThe mini-max method of gameplaying. The alpha-beta speedupalgorithm. Heuristic pruning.Static evaluation and plausiblemove generation.


Using EvidenceRemarks on strategy and tactics.Learning to play better. Linearscoring sums. Signature tablesand layered signature tables.


Probing A New DomainThe problem of line drawinganalysis. Combining regions in-to bodies. More evidence versusbetter evidence. Line drawinganalysis as a research paradigm.


Exploiting ConstraintsIdentifying illegal drawings.Classification of lines and ver-texes. Searching for compatibleand vertex interpretations.


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ARTIFICIAL INTELLIGENCE - Continued

Working Out An EpistemologyHandling shadows and cracks.Using illumination information.Coping with small infinities.The metatheory of descriptionrefinement.

32-min. Color' Videotape17-0111 Purchase $285 Rental $29.

LearningDescription based learning ofstructures from samples. Theimportance of the near-miss.Model refinement using emphaticrelations. Hypothesis and con-tradiction. Learning by dis-covery, from examples, and bybeing told.


Identifying Structures and Con-textComputing relations between ob-jects. Plain and fancy ident-ification. Searching throughsimilarity networks. Framesystems and contexts.


LISP Basics (1)Basic numeric and symbol-manipulating primatives. Valuesand properties. The need forquoting. Predicates and con-ditionals. Defining new.functions. Recursion.


LISP Basics (2)Free and bound variables.MAPCAR, APPLY, and LAMBDA. Cal-culating the depth of an S-expression. Finding the mini-max value of a tree.

33-min. Color. Videotape17-0115 Purchase $290 Rental $29.

Differentiation in LISPThe identical form of programsand data. Constructing new S-expressions'from pieces of oldones. Simplification on thefly. Intermediate expressionbulge.


Building A Matching LanguageUsing LISPStoring and Retr:ieving in-formation using property lists.Matching patterns against knownfacts. Storing facts inindexed directories.


Improving The Matching FunctionSimultaneous matching andvariable assignment. Matchingpattern elements againststrings. Restricted matching.


ARTIFICIAL INTELLIGENCE - CompiNV Set

Color Videotapes

Complete set of twenty-four colorvideotapes.

17-1100 Purchase $5825 (SAVE $940)120 Day Rental *607 (SAVE $74)

Suggested Text

The Psychology of ComputerVision, edited by P. H. Winston,McGraw-Hill, 1975.282 pp.

17-3100 Purchase $18 each.

Study Guide

Comments, photographs, refer-ences, problems, solutions.182 pp. (One per studentrecommended.)

17-2100 Purchase $8.00 each.(10% Discount on five or more)

A Complete Serf-Study Subject.The sat of videotapes describedabove can be wed as a complete seif-study subject when accompanied by theStudy Guide and Suggested Text.

4

Working Algebra Word ProblemsTranslation of sentences intoequations. Breaking up com-pound sentences. Retrievinglibrary facts. The toypsychiatrist program.


Demons and Automatic BackupThe MICRO-PLANNER Language.Consequent, antecedant, anderasing subroutines. Lookingfor a fallible sinner.


Understanding EnglishThe role of syntax, semantics,and deduction. The structureof noun groups. Translatingnoun groups into MICRO-PLANNERprograms.


Effecting English Commands inthe Blocks WorldGoal oriented programming. Theheterarchical approach. Puttingthe pyramid on the green block.


Constraint StructuresSets of mutually exclusivefeatures. Entry conditions.A 0th order theory of semantics.Bouncing the pointed ball.


Aspects of Natural LanguageSyntaxContext free and transformation-al grammars. Systemic grammarand feature driven analysis.Special purpose languages fordealing with syntax. Picking upa big red box.


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CalculusHerbert I. Gross

Calculus covers the material norm-ally found in the first two yearsof a modern college sequence incalculus, differential equations,and linear algebra. The coursebegins with elementary set theoryand other aspects of "new math"and continues with differential andintegral calculus, circular andtranscendental functions, andinfinite series. The courathencontinues with vector arithmeticand vector calculus, partialderivatives, matrix algebra, andmultiple integration. The final

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part of the course covers complexvariables, differential equations,and linear algebra.

Designed originally as a refreshercourse (and, in fact, calledCalculus "Revisited" when used atMIT), this material is suitable forall students with the requisitebackground.

Herbert I Gross was Senior Lec-turer, Massachusetts Institute ofTechnology.

kt.

Calculus

Preface to CalculusAn introduction to calculus; theconcept of 0/0; instantaneousspeed; introduction to functiOnsand graphs; the limit concept;area; general overview of calculus.

32-min. B&W Film or Videotape26-0000 Purchase $215 Rental $22.

Sets, Functions, and LimitsSix B&W 16mmFilms or Videotapes

Analytic GeometryCartesian coordinates; curves assets of points; graphs of func-tions; equations of straightlines; simultaneous linearequations.

37-min. B&W Film or Videotape26-0101 Purchase $240 ,Rental $24.

FunctionsNotations; concepts of onto andone-to-one; the arithmetic offunctions of a real variable;intervals and deleted neighbor-hoods; absolute values; compo-sition of functions.

39-min. B&W Film or Videotape26-0102 Purchase .$255 Rental $2f.

Inverse Functions, "Switch inEmphasis"The concept of an inverse func-tion; some examples; graphicalinterpretation; single-valuedand multi-valued functions; adiscussion of branches of func-tions.


SETS, FUNCTIONS, AND LIMITS - Complete Set

Films/Videotapes

Complete set of six B&W16 mm films or videotapes

26-1100 Purchase $1600 (SAVE $140)30 Day Rental $166 (SAVE $10)

Suggested Text

Calculus and Analytic Geometry(Fourth Edition) by G.B. Thomas,Addison-Wesley, 1968, 818 pp.

26-3000 Purchase $16.95 each.

Supplementary Notes

A supplement to the text, cover-ing "new math" concepts andexpanding on difficult topics inCalculus of a Single Variable.346 pp.


Study Guide

Pretest, reading assignments,problems, solutions, quiz.184 pp. (One per studentrecommended.)

26-2100 Purchase $6.00 each.(10% Discount on five or more.)

Lecture Notes

A set of chalkboard photographsfor all the films/videotapes onCalculus of a Single Variable.82 pp.


A Complete Self-Study Subject.The set offilms/Videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Lecture Notes, Sug-gested Text, and Supplementary Notes.

7

8

SETS, FUNCTIONS, AND LIMITS - Continued

Derivatives and LimitsInstantaneous speed as an out-growth and refinement of averagespeed; definition of limit;instantaneous speed as a limit;the formal definition of limitand some consequences.


A More Rigorous Approach to LimitsA continuation of the previouslecture; important limit pro-perties are developed as theoremsfrom the formal definition oflimit.


Mathematical InductionThe meaning of mathematicalinduction; some examples of whatmathematical induction is andisn't; applications to limittheorems.


DIFFERENTIATION - Complete Set

Films/Videotapes

Complete set of eleven B&W16 mm films or videotapes.


Suggested Text



Supplementary Notes



DifferentationEleven B&W 16mnFilms or Videotapes

Derivatives of Some Simple FunctionsDefinition of derivative; thederivative of xn where n is aninteger; derivatives of sums,differences, products, andquotients.


Approximations and InfinitesimalsApproximating. Ay by f'(x)Ax;discussion of the differencebetween Ay and f'(x)Ax; someexamples; introduction to the chainrule.


Composite Functions and theChain RuleComposition of functions; a.graphical interpretation; applica-tions to parametric equations;using the chain rule to extendour concept of finding derivatives.


Study Guide

Pretest,-reading assignments,problems, solutions, quiz.268 pp. (One per studentrecommended.)

26-2200 Purchase $8.50 each.(10% Discount on five or more).

Lecture Notes.



A Complete Self-Study Subject.The set of'films/Videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide Lecture Notes, Sug-gested Text,. and Supplementary Notes

8

Differentiation of InverseFunctionsThe concept of an inverse function;differentiation of an inverse func-tion; when is a function invertible?


Implicit DifferentiationFinding the derivative when thefunctional relationship is implied(that is, when it has the formf(x,y) = 0]; application to thecase of xn where n is a rationalnumber; the use of implicitdifferentiation in the study ofrelated rates.


ContinuityPhysical internretation ofcontinuity; th, ofcontinuity in terms of limits;a geometric interpretation ofcontinuity; some applicationsof continuity to equationsolving; some analytic conse-quences of definition ofcontinuity.


Curve PlottingBasic pre-calculus review; evenand odd functions and other .

symmetries; the role of the firstand second derivatives in curveplotting; stationary points;inflections; some examples.


Maxima and MinimaHigh and low points of a curve;techniques for finding these highand low points; applications tofinding maxima and minima of func-tions; some physical applications.


Rolle's Theorem and itsConsequencesStatement of Rolle's Theorem; ageometric interpretation; somecautions; the Mean Value Theorem;consequences of the Mean ValueTheorem.


Inverse DifferentiationThe "Opposite" of differentiation;trying to find f(x) knowing f'(x);some examples; some formulas;notation.


The "Definite" Indefinite Integral'

b

The meaning of Ji f(x) dx as

ag(b) - g(a) where g'(x) = f(x);some applications.


The Circular FunctionsTwo B&W 16mmFilms or Videotapes

Circular FunctionsTrigonometric functions withoutthe use of angles; the logic ofradian measure; the definition ofcircular functions; the derivativeof sin x and cos x.


Inverse Circular FunctionsMeaning of arcsin x in terms of thesine function; the derivative ofarcsin x in terms of the derivativeof sin x; some applications.


Study Guide



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10

The Definite IntegralFour B&W 16mmFilms or Videotapes

The Definite IntegralAxiomatic approach to area; areaapproximations by upper and lowerbounds; the method of exhaustion;using limits to find areas of non-rectilinear regions; piecewisecontinuity; trapezoidal approxi-mations.


Marriage of Differential andIntegral CalculusFirst Fundamental Theorem ofIntegral Calculus, some applica-tions; Second Fundamental Theoremof Integral Calculus; someapplications; significance of thetwo theorems.


3-Dimensional AreaExtending the axioms of area tovolume; some applications; themethod of cylindrical shells.


THE DEFINITE INTEGRAL - Complete Set

Films/Videotapes

Complete set.of four B&W16 mm Films or Videotapes.

26-1400 Purchase $870 (SAVE $75)20 Day Rental $ $86 (SAVE $10)

Suggested Text



Supplementary Notes

A supplement to the text, cover-ing "new math" concepts andexpanding on difficult topics inCalculus of a Single Variable346 pp.


1-Dimensional AreaThe main difference betweenarclength and either area orvolume; the limit definition ofarclength; some philosophical andpractical questions concerningthe definition; approximatingerrors and their magnitude whenwe use infinite sums.


Transcendental FunctionsFour B&W 16mmFilms or Videotapes

Logarithms without ExponentsThe concept of the naturallogarithm; the notion of the rateof change being proportional tothe amount.,yeesent; the generalconcept of'6: logarithmic function;the study of ln x in terms ofdifferential calculus; the studyof ln x in terms of integralcalculus; the meaning of thenumber e as the base of thenatural logarithms.


Study Guide



Lecture Notes


26 -5000 Purchase $4.50 each.

A Complete Sell-Study Subject.The set of films/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Lecture Notes, Sug-gested Text, and Supplementary Notes.

10

11

Inverse LogarithmsThe invertibility of thelogarithmic function; ex as theinverse of In x; a discussion ofexponential functions; someapplications.


What a Difference a Sign MakesHyperbolib functions in terms ofthe hyperbola x2-y2=1; compari-sons with the circular functions;the relationship between hyperbolicfunctions and exponential func-tions; applications of calculusto hyperbolic functions.


Inverse Hyperbolic FunctionsThe theory of inverse functionsapplied to the hyperbolic func-tions; some formulas for dif-ferentiation and integration; someapplications.


More Integration TechniquesFour B&W 16mmFilms or Videotapes

Some Basic RecipesA review and extension of previousresults for finding f(x) knowingf'(x); particular emphasis isplaced on the case where f'(x)involves the sum and/or differenceof two squares; completing thesquare.


Partial FractionsThe concept of partial fractions;finding f(x) when f'(x) is thequotient of two polynomials; somenotes about identities; applicationof partial fractions to the casewhere f is of the formf(sin x, cos x).


TRANSCENDENTAL FUNCTIONS - Complete Set

Films/Videotapes

Complete set of four B&W16 mm films or videotapes


Suggested Text



Supplementary Notes



Study guide

Pretest, reading assignments,problems, sontions, quiz.90 pp. (One per studentrecommended.)


Lecture Notes



A Complete Self-Study Subject.The set of films/videotapes describedabove can-be used as a complete self-Study subject when accompanied bythe. Study Guide, Lecture Notes, Sug-gested Text, and Supplementary Notes.

11

12

MORE INTEGRATION TECHNIQUES - Continued

Integration by PartsUsing the identityd(uv) = v + vdu to find Judyknowing vdu; using the techniqueto evalu to certain integrals;reduction formulas; someapplications.


Improper IntegralsThe problem of trying to study

If(x)dx when f(x) is not

continuous on the interval [a,b];some examples; what happens if thelimits of integration are notfinite; importance of improperintegrals.


Infinite SeriesSix B&W 16nrrn

Films or Videotapes

Many Versus InfiniteDiscussion of how infinity differsfrom "very large"; some subtle andnot subtle consequences of thedifference; the case againstintuition; motivating infiniteseries in terms of finding areaas a limit.


Positive SeriesThe special case wherein each termin the series is non-negative; theconcept of convergence; thecomparison test; the ratio test;the integral test.

34-min. B&W Film or VideOtape26-0702 Purchase $225 Rental $23.

MORE INTEGRATION TECHNIQUES - Complete Set

Films/Videotapes 11

Complete set of fotr B&W16 mm films or videotapes.

26-1600 Purchase $/25 (SAVE $65)20 Day Rental $73 (SAVE $10)

"Suggested Text

Calculus and Analytic Geometry(Fourth gdition) by G.B Thomas,Addison-Wesley, 1968, 818 pp.


Supplementary Notes



Study Guide


26-2600 Purchase $4.00 each.AJA4 Discount on five or more.)

Lecture Notes



A Complete Self-Study Subject.The set of films/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Stuck Guide,'Lecture Motes, Sug-,gested Text, and Supplementary Notes.

12

13

Absolute ConvergenceDiscussion of non-absoluteconvergence; conditional and .

absolute convergence; thesubtlety of a series convergingWhen each of its negative termsis replaced by the absolute valueof tha.t term; some consequencesof absolute convergence; geometricinterpretation.


Polynomial ApproximationsUsing an nth degree polynomial toapproximate a function f(x); howto choose the coefficients of thepolynomial to vet the "best"approximation; the notion of apower series; interval ofconvergence of a power series;Taylor's Remainder Theorem;expressing functions in terms ofpower series.


INFINITE SERIES - Complete Set

Films/Videotapes

Complete set of six B&W16 mm films or videotapes.


Suggested Text



Supplementary Notes



Uniform ConvergenceA discussion of pointwise con-vergence versus uniform con-vergence; some importantconsequences of uniform con-vergence; applications ofuniform convergence to the studyof power series.


Uniform Convergence of PowerSeriesThe topics introduced in theprevious lecture are extendedhere. In particular theWeirstrass M-test is introducedand discussed; using power seriesto evaluate definite integralswhen we do not know the anti-derivative of the integrand.


Study Guide


26-2700 Purchase $6.00 each.(10% Discount on five or more.),,

Lectures Notes



A Complete Self -Study Subject.The set of films/videotapes describedabo0e can be used as a complete safstudy subject when accompanied bythe Study Guide, Lecture Notes, Sug-gested Text, and SUpplementary Notes.

1413

sector ArithmeticSix B &W 16mmFilms or Vi.leotapes

:.='The "Game" of MathematicsThe generalized definition of agame; mathematics as a "game";mathematical structure viewed asa "game".


"Arrow" ArithmeticDefinition of a vector; vectorsas directed lengths (arrows);Mdition of vectors (the result-antY;,i and j components; anintroduction to vector arithmeticin terms of mathematical struc-ture.


3-Dimensional VectorsGeneralization from 2-dimensionalspace to 3-dimensional space;i,j, and k components of vectors;vector arithmetic in 3-dimensionalCartesian coordinates; othercoordinate systems; vector pro-perties versus coordinate pro-perties.


VECTOR ARITHMETIC - Complete Set

Films/Videotapes

Complete set of six B&W16 mm films and videotapes.


Suggested Text



Supplementary Notes

A supplement to the text intro-ducing the concept of mathematicalstructure and expanding on dif-ficult topics in Calculus ofSeveral Variables. 182 pp.


The Dot ProductPhysical motivation in terms of"work"; the geometric definition;computing the dot product inCartesian coordinates; themathematical structure of thedot produCt; geometric applica-tions to finding angles andlength projections.


The Cross ProductGeometric definition; the struc-ture of the cross product;computing the cross product inCartesian coordinates; usingdeterminant notation to computethe cross product; geometricapplications of the crossproduct to finding areas andlines perpendicular to planes.


Equations of Lines and PlanesVector methods for finding theequation of a line in 3-space;finding the equation of a planein terms of vectors; someexamples.


Study Guide

Pretest, chalkboard photographs,reading a'Asignments, problems,solutions, quiz. 173 pp. (Oneper student recommended.)


A Complete Self -Study Subject.The set of-films /videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, SuggePted Text, andSupplementary Notes.

14

15

Vector CalculusFour E37.,' 16mm

V-7:1e2tareo

Vector Functions of a ScalarVariableTh6 concept of "operating" on anumber to produce a vector;force as a function of time;limit theorems; the derivativeof a vector function of a scalarvariable; some formulas forfinding derivatives; applicationto motion in a plane.


Tangential and Normal VectorsThe position vector; the unittangent vector; the unit normalvector; the concept of curvatureand radius of curvature; thetorsion vector in 3-dimensionalspace.


VECTOR CALCULUS - Complete Set

Films/Videotapes

Complete Set of four B&W16 mm films and videotapes.

271200 Purchase $760 (SAVE $65)20 Day Rental $76 (SAVE $10)

Suggested Text



Supplementary Notes -


27-4000 Purchase $5.00

Polar CoordinatesDefinition of polar coordinates;the relationship between polarand Cartesian coordinates; polarequations for curves; slope andarea in terms of polarcoordinates.


Vectors in Polar CoordinatesThe basis vectors in polarcoordinates; the need for usingpolar coordinates in some vectorproblems; the position vector,the velocity vector, and theacceleration vector in polarcoordinates; applications to acentral force field.


a

Study Guide

Pretest, chalkboard photographs,reading assignments, problems,solutions, quiz. 212 pp. (Oneper student recommended.)


A Complete Self-Study Subject.The set of films/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Suggested Text, andSupplementary Notes.

15

16

Partial DerivativesSix B&W 16mmFilms or videotapes

n-Dimensional Vector Spaces.The concept of a vector as theindependent variable; a scalarfunction of a vector variable;the structure of an n-dimensionalvector space; an example of a4-dimensional vector space;generalizing the concepts ofdistance and limits ton-dimensional vector spaces.


Calculus of Several VariablesThe special case of 2 independentvariables; a geometric interpre-tation; the concept of a partialderivative; some special cautions;the partial derivative in termsof "slices" of a surface; theconcept of a tangent plane to asurface.


PARTIAL DERIVATIVES - Complete Set

Films/Videotapes

Complete set of six B&W16 mm films and videotapes


Suggested Text



Supplementary Notes



Directional DerivativesMotion in a direction other thanparallel to either the x- ory-axis; the definition of adirectional derivative in termsof Cartesian coordinates; thegradient vector; the tangentplane; some examples ofdirectional derivatives.

33-min. B&W Film or Videotape27-0303 Purchase $220 Rental $22':'

The Chain RuleGeneralizing the Chain. Rule to afunction of several realvariables; using the chain rule tofind higher order derivatives;some examples.


Integrals Involving ParametersPhysical motivation; geometricinterpretation; differentiating

ff(x,y) dy; variable limits of

a

integration; some subtleties.


Study Guide



A Complete Self-Study Subject.The set offUms/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, S4ggested Text, andSupplementary Notes.

16

17

Exact DifferentialsThe differential of f(x,y); thedefinition of the total dif-ferential; the meaning of anexact differential; applicationsto equations of the form f(x,y)=0


Matrix AlgebraFive B&W 16mTFilms or Videotapes

Linearity RevisitedProperties of linear functions;the concept of "locally" linearusing the linear part of w tostudy w = f(x,y) in "small"neighborhoods; systems of linearequations; matrix notationmotivating matrix multiplication.


MATRIX ALGEBRA - Complete Set

Films/Videotapes

Complete set of five B&W16 mm films or videotapes


Suggested Text



Supplementary Notes

A supplement to the text intro-ducing.the concept of nathematicalstructure and expanding on dif-ficult topics in Calculus ofSeveral Variables. 182 pp.


The "Game" of Matricesn by n matrices; defining equalityof two matrices; adding twomatrices; -structural propertiesof matrix arithmetic; somedifferences tvtween matrix andnumerical arithmetic; non-singular matrices,;. introductionto matrix algebra; using de-terminants to study non-singularmatrices.

41-min. B&W Film' or Videotape27-0402 Purchase $265 Rental $27.

Inverting a Matrix'Finding the inverse of a non-singular matrix; interpretationin terms of matrix algebra,functions, and geometry; discus-sion of when a matrix is singularhow to determine whether a matrixCan be inverted.


Inverting More General Systemsof EquationsA review of inverting linearsystems; inverting more general(i.e., non-linear) systems; theJacobian; some examples; discus-sion of various pitfalls.


Study Guide

Pretest, chalkboard photographs,. reading assignments, problems,solutions, quiz. 262 pp. (Oneper student recommened.)

27-2400 Purchase $8.50 eacj.(10% Discount on five or afore.)

A Complete se*study subJect.The set of filme/videopapes describedabove can be used as a acmplete self-

study subject wham accoMpanied bythe Study (kids, Suggested Text, andSupplementary Notes.

17

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MATRIX ALGEBRA - Continued

Maxima and Minima in SeveralVariablesThe meaning of relative maxima andand minima in the study of real-valued functions of several realvariables; how to test for suchvalues; a geometric interpreta-tion; constraints and the useof the chain rule.


Multiple IntegrationFive B&W 16mmFilms or Videotapes

Double Multiple SumsPhysical motivation in terms ofvariable density; geometricinterpretation; application tofinding the mass of a squareplate; upper and lower bounds;generalization; multiple sumnotation limits involvingmultiple sums.


MULTIPLE INTEGRATION - Complete. Set

Films/Videotapes



Suggested Text



Supplementary Notes



The Fundamental TheoremThe anti-derivative in severalvariables; some examples; ageometric interpretation in termof areas; computing limits ofcertain infinite double sums bymeans of the anti-derivative andconversely.

-26-min. B&W Film or Videotape27-0502 Purchase $175 Rental $20.

Multiple Integration and theJacobianA review of the definite integraland change of variable; anexample; the problem when we dealwith more than one independentvariable; mapping a region ofthe xy-plane into a region in theuv-plane; the role of the Jacobianin change of variable problemsinvolving multiple integration.


Introduction to Line IntegralsThe definition of a line integral;distinguishing a line integralfrom a double integral; someexamples; some general propertiesof line integrals; viewing theline integral as a definiteintegral.


Study Guide



A Complete Self-Study Subejct.The set offilms/videotapeo describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Suggested Text, andSupplementary Notes.

18

19

Green's TheoremA discussion of simply-connectedregions; the statement of Green'sTheorem; an outline of the proof;some comments about the theoremshowing how line integrals maybe related to multiple integrals;some examples; applying Green'sTheorem to regions which arenot simply-connected.


Complex VariablesFive BMW 16mmFilms or Videotapes

The Complex NumbersDevelopment of the real numbers;complex numbers as a naturaloutgrowth of the real numbers;arithmetical structure; polarcoordinates and complex numbers;applications; DeMoivre's Theorem;extracting the nth roots of anumber.


COMPLEX VARIABLES - Complete Set

Films/Videotapes



Suggested Text



Supplementary Notes

A supplement to the text,providing background informationon number systems and expandingon the concepts of linear inde-pendence and differentialoperators. 92 pp.


, Functions of a Complex VariableRules which assign complex numbersto other complex numbers; ageometric interpretation; ananalytic and graphical introduc-tion to limits; derivatives ofcomplex functions; Laplace'sequation.


Conformal MappingsReview of mappings of the xy-plane into the uv-plane; thedefinition of a conformal map-ping; applications; conformalmapping in the study of Laplace'sequation; boundary valueproblems.


Sequences and SeriesThe concept of sequences andseries applied to complexnumbers; a pictorial interpreta-tion; defining sin z, log z, etc.in terms of convergent powerseries; application to seriesof real numbers;interva1 ofconvergence.


Study Guide

Pretest, chalkboard photographsreading assignments, problems,solutions, quiz. 370 pp.(One per student recommended.)


A Complete Self -Study Subject.The set of filatelvideotapes describedabove can be used as a complete self -

study subject Ohm accompanied bythe Study Guide, Suggested Text, andSiOlgewentar0 !Votes.

19

20

COMPLEX VARIABLES - Continued.

Integrating Complex FunctionsA review of the definite integral;extending the results to thecase of complex numbers; lineintegrals; integrating analyticfunctions; integrals alongclosed curves.


Differential EquationsSeven B&W 16mmFilms or Videotapes

The Concept of a General SolutionGiven f(x,y,y') does the equationhave a solution and if so is thesolution unique? Some examples.Clairaut's Equation. Thedefinition of a general solution.Application to certain firstdegree differential equations.More on exact differentials.


Linear Differential EquationsExamples of non-linear differentialequations; the definition of alinear differential equation;some examples; properties oflinear equations; finding thegeneral solution of a lineardifferential equation.


Solving the Linear EquationL(y) = 0; Constant CoefficientsTrying for solutions in the form

y = er ; the problems involvedwith r being a non-real number;the general concept of thereduced or homogeneous equation;what happens if r is a repeatedroot of the auxiliary equation;some examples.

19-min, B&W Film or Videotape28-0203 Purchase $130 Rental $20.

DIFFERENTIAL EQUATIONS - Complete Set

Films/Videotapes

Complete set of seven B&W16 mm films or videotapes


Suggested Text


26-3000 Purchase $16.95 each

Supplementary Notes

A supplement to the text,providing background informationon, number systems and expandingon'the concepts of linear inde-pendence and differentialoperators. 92 pp.

28-.4000 Purchase $4.00 each.

Study Guide

Pretest, chalkboard photographsreading assignments, problems,solutions, quiz. 458 pp.(One per student recommended.)


A Coarptete SeZP.Study Subject.The set offilms/Videotapes describedabove can be used as a oomplete self-study subject when accompanied bythe Study Guide, Suggested Text,- andA4ppiementary Notes.

20

Undetermined CoefficientsFind a solution of L(y) = f(x)in the special case that thecoefficients are still constantsand f(x) is either a polynomial,an exponential function, or afunction of the form sin mx or.cos mx. The meaning of un-determined coefficients; the roleof the reduced equation; themethod of guessing a trialsolution. Some applications.


Variation of ParametersA method for handling L(y) = f(x)for any linear equation and moregeneral categories for f(x); thederivation of the technique; howthe technique is used; someexamples; a discussion of whythis technique is so valuable.


Power Series SolutionsA review of previous techniques;a key existence theorem; usingpower series to find an existingsolution; some examples.


LINEAR ALGEBRA - Complete Set

Films/Videotapes

Complete set of eight B&W16 mm films or videotapes


Suggested Text



Supplementary Notes

A supplement to the text,providing background informationon number systems and expandingon the concepts of linear inde-pendence and differentialoperators. 92 pp.


Laplace TransformsFunctions of exponential order;the definition of the Laplacetransform of a function; computingthe Laplace transform of somespecial functions; some notes onLaplace transforms; the linearaspects of Laplace transforms;a key property about Laplacetransforms; applications tolinear differential equations;Lerch's Theorem.


Linear Algebia

Eight BallemmFilms or Videotapes

Vector SpacesAn axiomatic definition ofstructure; some importanttheorems; discussion of how theaxiomatic definition generalizesthe n-tuple definition; ageometric interpretation; theconcept of a subspace.


Study Guide

Pretest, chalkboard, photographsreading assignments, problems,solutions, quiz. 398 pp.(One per student recommended.)


A Complete Self -Study Subject.The set of films /videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Suggested Text, andSupplementary Notes.

2221

LINEAR ALGEBRA - Continued

Spanning VectorsDefinition of spanning vectors;some examples; the definition oflinear dependence and linear in-dependence; some examples; a newlook at the dimension of a vectorspace; constructive examples.


Constructing BasesReview of previous lecture;definition of a basis for a vectorspace; some important observations;constructing a basis for a givenvector space; the invariance ofthe dimension of a vector spacein terms of basis vectors; usingmatrices to show when one vectoris a linear combination of othervectors.


Linear TransformationsDefinition of a linear trans-formation; properties of lineartransformations; some examples;the relationship between lineartransformations and matrices;more examples; the matrix of alinear transformation relative toa particular basis.


DeterminantsInventing a technique for tellingus when n vectors can be thebasis of an n-dimensional vectorspace. The properties whichdefine a determinant; someconsequences of these properties;some examples and "short-cuts".


EigenvectorsSolving the vector equationf(v) = cv; geometric interpreta-tion; some applications; a matrixapproach to eigenvectors fromthe choice of a basis; someimportant invariants; someexamples.


Dot ProductsGeneralized properties of thedot product; examples; theGram-Schmidt orthogonalizationprocess; constructing an ortho-normal basis for a given vectorspace.


Orthogonal FunctionsOrthogonal functions; definitionof Fourier series; some specialcases; constructing the Fourierseries for some given functionsand a pictorial interpretation;a discussion of errors.


22 23

Colloid andSurface ChemistryJ. Th. G. Overbeek

Colloid and Surface Chemistryis a set of 55 lectures anddemonstrations on surfacechemistry, lyophobic colloids,electrokinetics and membranephenomena, and lyophilic colloids.

Interfacial phenomena play asignificant role in a large numberof processes in the chemical,petroleum, and metallurgicalindustries as well as in thebiological processes of lifeiteself. Lyophobic colloids --paints, dyes, coatings, cosmetics,pharmaceuticals, food products --also play an important role in

our daily lives. An understandingof electrokinetic phenomena hascontributed to a number ofanalytical techniques and indus-trial processes. And lyophiliccolloids not only include theextremely important polymers andreversible associates, but cons-titute the very basis for lifein the form of proteins andnucleic acids.

J. Th. G. Overbeek is Professorof Physical Chemistry at theUniversity of Utrecht in theNetherlands.

2.4

Colloid andSurface ChemistrySurface Chemistry

Sixteen B&W 16mmFilms or Videotapes

Introduction to Colloid Chemistryand its Relation to SurfaceChemistry and ElectrochemistryDisperse systems are of interestboth for their many applicationsand as systems worthy of fun-damental study. Their large inter-facial area explains why surfacechemistry and surface electro-chemistry are intrinsic facets ofcolloid chemistry.


Surface Tension and SurfaceEnergiesSurface tension results from aninbalance of intermolecularforces. Relations between surfacetension and (Helmholtz and Gibbs)surface free energies. Hydrostaticpressure (Young, Laplace) andmodified vapor pressure (Kelvin)at curved interfaces.

40-min. B&W Film or Videotape11-0102 Purchase 260 Rental $26.

Measurement of Surface andInterfacial Tensions ofLiquids (1)Static and dynamic measurementsrelated to curvature of ameniscus: capillary rise ordepression, maximum bubble pres-sure, stalagmometer (drop weight).


Measurement of Surface andInterfacial Tensions ofLiquids (2)Sessile or pendant drop or bubble,Wilhelmi plate, du Nouy ring,surface ripples, oscillating jet.

37-min. B&W Film or Videotape11-0104 Purchase$260 Rental $26.

Adsorption, Analytical AspectSurface or interface is a regionof finite thickness. Descriptionof (positive or negative) surfaceexcess with Gibbs dividing sur-face. Guggenheim method withtwo dividing surfaces. Invariantlinear combinations of surfaceexcesses.


Thermodynamics of Fluid InterfacesThe Gibbs adsorption equationand the concept of the surfaceexcess concentration. Importanceof -log c or -log a plots.Saturation adsorption. Criticalmicelle concentration.

48-min. B&W Film or Videotape11-0106 Purchase $305 Rental $31

Spreading - Surface Films ofInsoluble MonolayersSpreading tension, initial andfinal. Neumann's triangle.Influence of surfactants onspreading. Surface pressure.Langmuir trough, film balance.Surface equation of state, surfacepotential, surface viscosity andelasticity. Effect of monolayerson evaporation. Multilayers.


Surface Tension and SurfaceStructure of SolidsExperiments on surface tension.Calculation of surface (free)energies. Methods of determining.surface structure and modernspectroscopy and electronicanalytical methods. How toobtain large specific surface area.


24 25

Adsorption of Gases on SolidsPhysisorption, chemisorption.Adsorption isotherms, Langmuir,BET, Harkins and Jura, Polanyi,Frenkel, Halsey, Hill, de Boer(t-plot). Heterogeneity. Stepsin isotherms. Capillarycondensation, hysteresis, poresize distribution.


Chemisorption - Adsorption fromSolutionChemisorption, monolayer, largeheat of adsorption, Freundlich(Kuster) isotherm. Adsorptionfrom solution is always competi-tive. Determination of adsorption.Traube's rule (standard freeenergy of adsorption per CH2-group.


Adsorption from Solution,Continued. Contact AnglesAdsorption of polymers, of ions.Negative adsorption. Chromato-graphy. Contact angle. Influenceof surfactants. Wetting, dewet-ting, froth-flotation. Contactangle hysteresis.


SURFACE CHEMISTRY - Complete Set

Films/Videotapes

Complete set of sixteen B&W16 mm films or videotapes.


Suggested Text

Physical Chemistry of Surfaces byA.W. Adamson, Interscience,(Second Edition), 1967, 747 pp.


Energies and Entropy of AdsorptionRelations between r, Tr (or y) andc (or p). Calorimetric andisosteric heats of adsorption.Enthalpies and entropies inmodels, such as Langmuir, B.E.T.,mobile monolayer. Conversion ofadsorption isotherm into equationof state and vice versa.


Charged Interfaces - Electro-chemistry of the Phase BoundaryLippmann equation. Electro-neutrality of interfaces.Completely reversible and com-pletely polarizable electrodes.Potential determining ions.


Surface Potentials - Structure ofthe Electric Double LayerOuter and inner electric poten-tial difference. "Real potential."Double layer. Poisson-Boltzmannequation. Gouy, Chapman, Sternmodels. Thickness and capacityof double layer.


Study Guide

Lecture summaries and discus-sions, photographs, readingassignments, problems, andproblem solutions. 278 pp.(One per student recommended.)


A Complete Self-Study Subject.The set of films/videotapes describedabove can he used as a complete self-study subject when accompanied bythe Study Guide and Suggested Text.

2625

SURFACE CHEMISTRY - Continued

A Few Special Aspects of DoubleLayersNegative adsorption of co-ions.Ion-exchange. Point of zerocharge. Double layers in ioniccrystals and semiconductors.Rate of charge adjustment.


Free Energy of Double Layers -ElectrocapillarityCalculation of surface free

r energy: Chemical and electricalparts. Electrocapillary curve.'Charge and capacitance forHg /aqueous solutions. Otherdouble layers: inorganics, oil,and-gas, all against water.

55 min. B&W Film or Videotape11-0116 Purchase $385 Rental $39.

Lyophobic ColloidsFifteen B&W 16mmFilms or Videotapes

Introduction on Stability ofLyophobic ColloidsSize Range (lnm 1Pm) of col-loidal particles...distinctionbetween lyophobic and lyophiliccoldoids...emphasis on stabilityand coagulation (= flocculation)of lyophobic colloids and othergeometries.


Interaction Between Two DoubleLayersTwo parallel flat double layers...Poisson-Boltzmann equation...constant charge or constantsurface potential...change inGibbs free energy...Langmuir'sforce method...Stern correction.


Interaction Between SphericalDouble Layers - Schiller Layersand Other Experiments on DoubleLayer InteractionDerjaguin's method for spheres...small separations...largeseparations...Schiller layers,Tobacco mosaic virus, lipid layers.


Van der Waals ForcesVan der Waals forces responsiblefor long range attraction...additivity...flat plates,spheres.


Van der Waals Forces - Influenceof a Medium - Retardation -Lifshitz Method - ExperimentsVan der Waals forces betweenparticles in a medium alwaysattractive...retardation atlarge distances...Lifshitz'approach...experiments.

39-min B&W Film or Videotape11-0205 Purchase $255,Rental $26.

Combinations of Attraction and,,,.Repulsion - Application toColloid StabilityPotential energy curves...rule ofSchulze and Hardy...flocculationseries...DLVO theory...ions withabnormal flocculating power...irregular series...charge reversal.


Colloid Stability - LyotropicEffects - RepeptizationInfluence of lyotropic series onflocculation...requirements forreversibility (repeptization)...secondary minimum...mutualflocculation.


262`7

Foams and Soap Films (1)Coarsening of foams by diffusion,drainage, and breaking...colorand thickness of soap films...black soap films...self-healingGibbs-Marangoni effect...drainage mechanisms...Van derWaals and repulsive forces.


Foams and Soap Films (2)Second black films...foambreakers...light scattering andbreaking due to surface fluctua-tions...sharp transition ofcolored (silver) to blackfilms...applications of foams.


Emulsions - Suspensions inNon-Aqueous MediaEmulsions stabilized by surfactantsor by finely divided solids...creaming, coalescence, breaking...0/W and W/0 emulsions...inversion...applications of emulsions...non-aqueous suspensions: stabi-lity, as affected by electrolytes,permitivity, andparticle concentration...applica-tions.


LYOPHOBIC COLLOIDS - Complete Set

Films/Videotapes

Complete set of fifteen B&W16 mm films or videotapes.

11-1200 Purchase $3840 (SAVE $575)75 Day Rental $399-(SAVE $44)

Suggested Texts

Physical Chemistry of Surfaces byA.W. AdaMson, Interscience,(Second Edition), 1967, 747 pP.


Colloid Science Volume 1 editedby H. R. Kruyt, Elsevier Publish-ing COmpany, 1974, 389 pp.

11.-3200 Purchase $24C0t each

Steric Stabilization - SensitizedFlocculationStabilization by adsorbed polymers...anchor and tail (or loop)...repulsion by osmotic effect andby restriction of possible con-formations...examples...sensitizedflocculation due to bridging...applications.


Coarse Suspensions - RheologySediment density and flow behavioras funciton of suspensionstability...thixotropy...gelformation by flocculation oraddition of third phase...applications.


Sol Preparation, Dialysis andUltrafiltrationDispersion and condensationmethods...preparing isodispersesols...dialysis, electrodialysis,ultrafiltration...demonstrationof preparation of several sols...spontaneous emulsification.


Study Guide

Lecture. sUmmarle4 andSlone, photographer readingeissignmentS, PrObiemer andProblem solutions: 302 PP.(One per student recommended.)

11-2200 Purchase $13.00 each.(10% OlScount on five or more-)

A ampieteSW414M44, Subject.The set of fitixtivid±201,Wee describedabove can be 401414 air -GoViete Oaf-etudY eubjact when awartkorted bythe Study Cade and gaggeeted Text.

27

28

LYOPHOBIC COLLOIDS - Continued

Particle Size Determination -OpticsMicroscope...sedimentation...Coulter counter...electron-microscope...ultramicroscope...Tyndall light...Rayleigh and Mietheories...higher order Tyndallspectra...birefringence...tactoids.


Kinetics of FlocculationRapid and slow flocculation...Von Smoluchowski's theory...extension by Fuchs to slow floc-culation...log W - log c curves...experiments...influence ofstirring.


Electrokinetics andMembrane Phenomena

Nine B&W 16mmFilms or Videotapes

Introduction. The FourElectrokinetic Effects. TheZeta-PotentialRelationships between liquidmotion and electric field nearan interface...Electroosmosis,electrophoresis, electrodeposition,streaming potential, streamingcurrent, migration potential.


Theory of ElectrophoresisInfluence of Ka (K = reciprocalthickness of double layer, a =radius of particle) on electro-phoretic mobility.. Relaxationeffects.

29-min. B&W Film or Videotape11-0302 Purchase $195 Rental $20. -

Applications of ElectrokineticsInfluence of counterion chargeand concentration on zeta-potential...Concept of "slipping plane"...Techniques for determiningelectrophoretic mobility and forpreparative electrophoresis...Applications, including firehazards of high streaming poten-tials, separation of proteinmixture, concentrating sols byelectrodecantation, electro-deposition of latex and pigmentsfrom suspensions.


Non-Equilibrium ThermodynamicsApplied to Electroosmosis andStreaming PotentialEntropy production in irreversi-ble phenomena...Fluctuations...Onsager's reciprocal relations..Saxen's relation between

electroosmosis and streamingpotential. ,


Schmid Membrane Model. Non-Equilibrium Thermodynamics ofElectrophoresis and SedimentationPotentialIn Schmid model for membraneis replaced by density of fixedcharges...Electrophoresis andsedimentation potential con-nected by Onsager relation...Concentration dependence of rateof sedimentation.


Introduction to MembranePotentialsTreatment based on galvaniccell reaction...Reversibleelectrodes or salt bridges.


2829

Membrane Potentials. IncompleteSelectivity; B3 -Ionic Potentials;Filtration through MembraneSelectivity based on fixedcharge of the membrane...Meyer-Sievers - Theorell theory of itcomplete selectivity...Bi-ionicpotentials...Desalination byelectrodialysis...Flow of ions,solvent, electric currentthrough membrane.


The Donnan EquilibriumDonnan treatment of distri-bution of ions, osmoticpressure and membrane potential...Non-ideality based oninhomogeneity of Donnan phase.


The Donnan Potential. TheSuspension EffectDonnan potential treated as aseries of three diffusionpotentials...Importance of con-tributions of liquid junctionswith saturated KC1..Thesuspension (Wiegner-Pallmann)effect.


ELECTROK/NETICS - Complete Set.

Films/Videotapes

Complete set of nine B&W16 mm films or videotapes.

11-1300 Purchase $2065 (SAVE $230)45 Day Rental $217 (SAVE $16)'

Suggested TextColloid Science Volume 1 Editedby H.R. Rruyt, Elsevier Publish-ing Company, 1574, 389 pp.

11-3200 Purchase $26.00.

Lyophilic ColloidsFifteen B&W 16mmFilms or Videotapes

Introduction. Solutions ofLyophilic Colloids. Examplesof MacromoleculesSolutions of polymers...Surveyof biocolloids, synthetic poly-mers and polycondensates, theirrole in nature and fields ofapplication.


Polymer Synthesis. The Impor-tance of Polymers. Their Spe-cific RoleFree radical polymerization.Kinetic aspects. Pearl-andemulsion-polymerization. Ionicpolymerization. Stereo-regularpolymers. Polycondensation.Intra - and intermolecularforces, rubber elasticity, in-formation storage in biopolymers.


Statistics of Polymer Coil Con-formations. Viscosity of Poly-mer SolutionsRandom flight statistics. Dis-tribution function of end-to-end distance. "Statisticalchain element." Viscosity ofsolutions of coils.


Study Guide

Lecture summaries and discus-sions, photographs, readingassignments, problems,.andproblem solutions. 156 pP(One per student recoMMended.)

11-2300 Purchase $6.50 each(10% Discount on five or more.)

AComplAte0BWIf-Sti4The set of describedabove can be used ae aompiete self-etudy a:44feet when, asevevanied byMe Study Guide and Suggested Text.

30 29

LYOPHILIC COLLOI - continued

Rubber Elasticity.Force vs. elongation relationfor ideal rubber derived fromentropy change on deformation.Glass transition temperature.Brittle point.


Thermodynamics of Polymer Solu-tions. Osmotic PressureFlory-Huggins theory. Quasi-lattice model. Energy, entropyand free energy of mixing "Verydilute" solutions. Theta-tem-perature. Fractionation.


Molecular Weight Distributions.Determination of Average Molecu-lar Weight by Osmotic Pressure,Chemical Analysis, ViscosityIntegral. (or cumulative) anddifferential molecular weightdistributions. Different kindsof average molecular weights.Number average M. Viscosityaverage M.


LYOPHILIC COLLOIDS - Complete Set

Films/Videotapes

Complete set of fifteen B&W16 pm films or videotapes.

11-1400 Purchase $4125 (SAVE $615)75 Day Rental $430 (SAVE $48>

SuggeSted Text

Principles, of. Polymer Chemistry byPaul J. Flory, Cornell UniversityPress, 1971, 672 pp.

11..3400 Purchase $24.50 each.

Light ScatteringLight Scattering in Rayleighapproximation (size <A/20) givesmass-average M. Fluctuation theoryof light scattering. Non-ideal-ity of solutions. Zimm-plot.


The UltracentrifugeRate of sedimentation and diffu-sion. The Svedberg equation.Shape factor. Sedimentationequilibrium. Archibald method.Applications.


Polyelectrolytes. Examples,Titration Curves, ElectrophoresisExamples of natural and syntheticpolyelectrolytes. Titrationcurve gives information on elec-trical free energy of coil. Ti-tration of proteins. Iso-electricpoint.


Study Guide

Lecture summaries and.Oiscus-sions, ptotographs,assignments, Problems, andproblem solutions. 306 PP-(One per student recommended.)

11-2400 Purchime $13.00 each.(10% Discount on five or more.)

A ampieteStaf-Study, Subject.The eet of fibmioideotaPes Oummibedatom otm be mod as a catelete sett-study subjeat when addlatrentedthe Study Guide and Sefigeeted Text.

3031

Polyelectrolytes. Viscosity,Light Scattering, Osmotic Pressure,SedimentationThree causes for the electro-viscous effect are expansion ofcoils, deformation of doublelayer and mutual repulsion ofpolyions. Light scattering de-pends strongly on 0 and c.


Coacervation, Salting OutPrecipitation of polyelectro-lytes by organic non-solventsand electrolytes..."Salting out"...Lyotropic series...Propertiesof coacervates. Complexcoacer-vates between polycations andpolyanions...Double Schulze-Hardy rule. Incompatibility ofnon-charged polymers. Nucleo-proteins and globulins.


Complexcoacervates.Electrophoresis. Structure ofProteins and Nucleic AcidsBuchner-effect and decompositionin electrophoresis. Autocomplex-coacervation. Theory of complex-coacervation based on Flory-Huggins theory with addition ofelectrostatic interaction.Microencapsulation. Helicalstructures in proteins andnucleic acids. Denaturation.

59-min. 136,107 Film or Videotape

11-0412 Purchase $395 Rental $39.

Association Colloids. MicelleFormation. Phase DiagramsCritical micelle concentration.Size and shape of micelles. Lawof mass-action explains sharpc.m.c. Driving force for micelleformation mostly entropy based.Influence of salt concentrationof c.m.c. and micelle size.


Association Colloids. MicellarSize. Thermodynamics. Applica-tionsMicelle molecular weightbest by light scattering. Cor-rection for negative adsorptionof co-ions. Thermodynamics ofmicelle formation. Hartley,Debye, Stigter. Cell membrane.


GelsStructural requirements for gel-ation. Sharp gel point. Crystal-line regions as crosslinks.Syneresis. Soap gels, jelly andcurd. Swelling. "Memory" ofgels. Theory of swelling. Poly-electrolyte gels. Mechano-chemistry.


A Visit with J. Th. G. OverbeekThe serious lecturer of theColloid and Surface Chemistryseries gives way to the warmhuman being behind the: theoriesand demonstrations. In an in-'terview with John T. Fitch of theMIT Center for Advanced Engineer-.ing Study, Theo Overbeek recountshis life story (baginning withhis "firm decision* not to be ateacher!) including the develop-ment of the D.L.V.O.theory.


32 31

Computer LanguagesMichael L. Dertouzos

Computer Languages: Structure andInterpretation focuses on issueswhich must be addressed in thedesign or implementation of anyprogramming system -- independentof its individual details. Theseissues include:

the means by which a variable isassociated with its value.

. the time at which the value ofa variable is calculated.

the logical power of a language

the efficiency and expressibilityof a language.

the use of functions to processother' functions.

. the translation of a languageinto the constructs of anotherlanguage.

The videotapes in this seriescomprise un-edited lectures andclassroom discussions as well asfour specially prepared studioproductions.

Michael L. Dertouzos is Professorof Electrical Engineering andComputer Science at MIT andDirector of the MIT Laboratory forComputer Science (formerly ProjectMAC).

Wrr

32

sousir.1

33

flileriO'f("Y

INN

Computer Languages

Thirty -nineColor Videotapes

Introduction to Computer ScienceThis lecture is a succinct answerto two basic questions:(1) What is computer Science?(2) How does it differ, in itsnature, from the other sciencesand engineering disciplines?In answering these questions, thelecture states the premises and .

goals of the course, and outlinesthe material that Will be covered.

:50-min. Color Videotape14-0101 Purchase $300 Rental $30.

Introduction to Machine LanguageEarly processor and memory accessmodels. Need for relative addres-sing, indirection, stacks, sub-routines. Overview of M machine(PDP-11) instruction set. Byte/word addressing. Execution cycle.


M Machine Languageme Addressing modes, instruction

formats. Types of instructions;opcodes. Examples. Octal vs.binary notation.

:50-min. Color Videotapeld-0103 Purchase $30Q Rental $30.

The Need for Subroutines & StacksBackus-Naur Form (BNF) as arecursive structure definition.Use of a stack for implementingrecursive programs. Examples.


Subroutines and Stack DisciplineStack operations. Stack disciplineand its importance. Mathematicalinduction. Subroutines; typesof call-return sequences. Methodsof passing parameters. The JSRand RTS instructions.

50 -min. Color Videotape14-0105 Purchase $300 Rental $30.

Assembly LanguageGoals of assembly language.Structure of A(M): lables,mnemonics, address calculation;Pseudo operations; symbolic expres-sions. ASCII codes; the name-value distinction.

Z50 -min. Color Videotape14-0106 Purchase $300 Rental $30.

Structure of AssemblersThe translation process. HowA(M) works; use of symbol tables.1 vs. 2 passes. Space-time trade-offs.


Applicative Expressions (AEs)Applicative vs. imperativefeatures of languages. Informalsyntax of AEs. Universe ofdiscourse. Informal semantics.

:50-min. Color Videotape14-0108 Purchase $3G0 Rental $30.

Meaning of AEsFunctionality. Development ofthe normal value algorithm fromintuitive notions of meaning.The substitution rule.

:50-min. Color Videotape14 -0109 Purchase $300 Rental $30.

Use of the Normal Value Algorithm.Evaluations using the nv algorithm.Free and bound variables. Condi-tionals, logic values.

2:50-min. Color Videotape14-0110 Purchase $300 Rental $30.

ConditionalsReview of free & bound variables.Different ways of implementingconditional operations. Impor-tance of not evaluating bothbranches. Augmentation of thenv algorithm.


3 433

COMPUTER LANGUAGES - Continued

Ramifications of Normal ValueRelativity of priviledged names.Implications of changes in orderof evaluation. Church-Rossertheorem explained intuitively.Control trees.

"z50-min. Color Videotape14-0112 Purchase $300 Rental $30.

Introduction to EnvironmentsMotivation for binding variablesto values in an environment. Theglobal environment; bind, lookupfunctions. Definitrniiiof theglobal environment evaluator(G-machine).

Z50-min. Color Videotape14-0113 Purchase $300 Rental $30.

Problems of the G-MachineReview of G-machine algorithm.Control trees, recursion in theG-machine. Demonstration ofidentifier collision.

z50-min. Color Videotape14-0114 Purchase $300 Rental $30.

The Stack Environment (S-Machine)Identifier collision as motivationfor a stack structured environment.Definition of the S-machine.Control trees.


Recursion in G & SExamples demonstrating theimplementation of recursiveprograms in global and stackenvironments. (Quiz review,)


Abstract RecursionThe advantages of recursion overiteration. Recursive programs innormal order. The fixed pointproperty; the Y operator.Examples.


Logical Power of ComputingSchemesThe theoretical notions ofcomputability and universalityare the central issues of thislecture. Topics coveredihclude:Turing machinescoding schemesproof that uncomputable functionsexistRussell's paradoxuniversality - the Church-Turingthesistests for universality


Recursive Function TheoryThis lecture continues the subjectof computability that was begunin Lecture 14-0118 by defining thecomputing scheme known as therecursive functions. Examplesof recursive functions areconstructed, and the importanceof the scheme is discussed.(Recursive function theory shouldnot be confused with recursiveprogramming.)

"z50-min. Color Videotape14-0119 Purchase $300 Rental $30.

Introduction to LISPPure LISP in relation to AEs.Arithmetic functions and predicates.COND syntax. The LABEL primitive.


S-ExpressionsS-expressions and the functionswhich operate on them. CAR, CDR,CONS. List notation.

:=60-min. Color Videotape14-0121 Purchase $300 Rental $30.

ListsLists and atoms. The pseudo-function QUOTE and its significance.Programming techniques for listprocessing functions.


34 35

Evaluators (1)Development of the S-machine(stack evaluator for AEs) writtenin LISP.


Evaluators (2)Conclusion of S-machine in LISP.Minimal pure LISP evaluatorwritten in LISP.


Evaluators (3)The classic EVAL-APPLY structuredLISP evaluator, in LISP. Extensi-bility of the model. Why QUOTEis not a function.

7:50-min. Color Videotape14-0125 Purchase $300 Rental $30.

Evaluators (4)Comparison of MPLEVAL, EVAL-APPLY,and normal order schemes. Levelsof evaluation. Implementation oflists. Box-pointer notation;sharing.


FUNARG Problems (SAW)Peculiarities of DELPHI LISP.Upward and downward FUNARG func-tional argument) problems as aconsequence of a stack-structuredenvironment. Motivation of treestructured environment.


Possible Cures for FUNARG ProblemsInformal usage of functionclosures (T-machine). Controltrees in the T-machine.


Tree Environment (1)Definition of T-machine in LISP,as a modification of theS-machine. Examples of usage.


Tree Environment (2)Upward funarg problem, as eval-uated by the T-machine. Sketchof equivalence proof for treemachine and normal order algorithm.


Imperative LISP (1)Syntax and semantics of SET, SETQ;DEFUN; motivation for and usageof, RPLACA, RPLACD.


Imperative LISP (2)Review RPLACA, RPLACD. Construc-tion of circular lists. Imple-mentation of SET and SETQ. Callby name; call by value. Callby reference.


SequencingThe primitives PROG2, PROGN.The PROG construct; RETURN, GO,labels. Motivate global labels(label closures).


Dynamic Allocation of StorageThe free storage list. Garbagecollection - marking and sweeping.Reference counters. The Deutschalgorithm.


Global Labels (1)The control state. Problemscaused by non-local GOs.Development of label closures assolution.


Global Labels (2)Application of global labels inerror handling, backtracking.Multiprocessing using labelclosures.


35

COMPUTER LANGUAGES Continued

Principles of TranslationRelation of translation tointerpretation. Efficiencyadvantages of translation.Translation of AE's to LISP.


AE's to Assembly Language (1)Overall plan - applicative toimperative schemes. Translationtime environments. Shallowbinding. Need for run-timeinterpretation.

7...:50-min. Color Videotape14-0138 Purchase $300 Rental $30.

AE's to Assembly Language (2)Continuation of previousrecitation with an exampleworked out.


COMPUTER LANGUAGES - Complete Set

Color Videotapes

Complete set of thirty-nineColor Videotapes


The following four videotapes arecolor studio productions. Thefirst two cover some of thematerial in the classroom lecturesand recitations listed above incompressed form. They can beused in place of the earlier tapesfor students with more programmingexperience. The second two tapesaugment the lectures and recita-tions and can usefully be shownin conjunction with them.

Machine LanguageCovers the material of 14-0102 and14-0103 in compressed form. Usesthe PDP-11 as an example of anactual machine. Topics includeorganization of the machine andits major components, the variousrepresentations of data, theexecution cycle of the machine,and the actions performed by asampling of the machine's instruc-tion repertoire:


Assembly Language, Subroutines,and StacksCovers the material of 14-0104,14-0105, and 14-0106 in compres-sed form. Includes symboliclabels and expressions, mnemonics,pseudooperations, subroutines.Motivates stacks as a means forstoring subroutine return points.Develops notion of stackdiscipline.


RecursionVisiting Professor Joseph Stoyexplains and demonstrates theprocess of writing recursiveprograms, i.e. programs thatinvoke themselves. Detailedexamples are illustrated (viz.three "monks" working on theTowers of Hanoi puzzle) andworked out to. clarify thisfrequently misunderstood topic.


DELPHIA demonstration of the.DELPHItimesharing system at a leveldesigned for the student with aminimum of previous computerexperience. Instruction includes:logging in and out, using theeditor and assembler, and usingthe LISP interpreter.

49-min. Color Videotape14-0204 'Purchase $370 Rental $37.

36

3 7

Digital SignalProcessingAlan V. Oppenheim

Digital Signal Processing is nowbeing applied to such diverseareas as biomedical engineering,acoustics, sonar, radar, seismology,speech communication, telephony,nuclear science, and image proces-sing. This widespread applicationhas been due, in large part, tothe advances in integrated circuittechnology which have had a pro-found impact on the techniquesfor transmitting and processingelectrical signals.

AIA

IA

This series of lectures and demon-strations begins with the defini-tion of discrete time signals andsystems. Topics covered includedifference equations, discretetime Fourier transforms, thez-transform, digital filterdesign and implementation, andthe fast Fourier transform.

Alan V. Oppenheim is AssociateProfessor of Electrical Engineeringand Computer Science at MIT.

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Digital Signal ProcessingTwenty-oneColor Videotapes

IntroductionProvides an overview of the courseand discusses some of the applica-tions of digital signal proces-sing.


Discrete-Time Signals andSystems (1)Definition of basic discrete-timesignals: The unit sample, unitstep, exponential and sinusoidalsequences. Definitions and repre-sentations of linear time-invariant discrete time systems.Properties of discrete-timeconvolution.


Discrete-time Signals andSystems (2)Stability and causality fordiscrete-time systems. Systemsdescribable by linear constant-coefficient difference equations.Frequency response of lineartime-invariant systems.


The Discrete-Time Fourier TransformGeneralization of the frequencyresponse representation ofsequences. Inverse Fouriertransform relAtion. Propertiesbetween continous-time anddiscrete-time Fourier transforms.


Sampling, Aliasing, and FrequencyResponseDemonstration of sampling andaliasing with a sinusoidal signal.Sinusoidal response of a digitalfilter. Dependence of frequencyresponse on sampling period.Periodic nature of the frequencyresponse of a digital filter..


Demonstration of Sampling,Aliasing, and Frequency ResponseDemonstrations (only) from above.


The Z-TransformRelationship between the Fouriertransform and the z-transform.Region of convergence for z-transforms. Relationship betweenregion of convergence, causalityand stability.


The Inverse Z- TransformTechniques for determining theinverse z-transform: inspectionmethod, use of power series expan-sion, partial fraction expansion,use of contour integration.


Z-Transform PropertiesGeometric determination of fre-quency response from pole-zeropatterns in the z-plane. Prop-erties of z-transforms: scaling,differentiation, shifting,convolution, etc.


38

33

The Discrete-Fourier SeriesFourier series representation forperiodic sequences. Determinationof Fourier series coefficients.Properties of Fourier Series.


The Discrete-Fourier TransformFourier representation of finitelength sequences. Relationshipbetween the Discrete-Fourierseries. Properties of the Discrete-Fourier transform: Symmetry,circular shifting, circularconvolution, etc.


Circular ConvolutionCircullar convolution of finitelength sequences. Interpretationof circular convolution as linearconvolution followed by aliasing.Implementing linear convolutionby means of circular convolution.


Representation of Linear DigitalNetworksBlock diagram representation ofdifference equations. Linearsignal flow graphs. Flow graphrepresentation of differenceequations. Matrix representationof digital networks. Computabilityof digital networks.


Network Structures for InfiniteImpulse Response (IIR) DigitalFiltersBasic network structures for IIRfilters: direct cascade andparallel form. Canonic structures.Transposition theorem for digitalnetworks and the resulting trans-posed forms.


Network Structures for FiniteImpulse Response (FIR) DigitalFilters and Parameter-QuantizationEffects in Digital FilterStructuresDirect form FIR filters. Efficientimplementation of FIR filters withlinear phase. Frequency samplingstructure. Effects of parameterquantization in digital filterimplementation.


Design of IIR Digital Filters (1)Transformation of analog filterdesigns to digital filter designs;Approximation of derivatives bydifferences. Impulse invariantdesign procedures.


DIGITAL SIGNAL PROCESSING - Complete Set

Color Videotapes

Complete set of twenty-oneColor Videotapes.


Suggested Text

Digital Signal Processing byA.V. Oppenheim and R. W. Schafer,Prentice Hall, 1975, 585 pp.


Study Guide

Chalkboard photographs, comments,reading assignments, problems,and problem solutions. 260 pp.(One per student recommended.)


A Complete Self-Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide and Suggested Text.

39

do

DIGITAL SIGNAL PROCESSING Continued

Design of IIR Digital Filters (2)Digital filter design using thebilinear transformation. Frequencywarping introduced by the bilineartransformation. Algorithmic designprocedures for IIR filters.


Examples of IIR Filter DesignDesign of digital Butterworthfilter using impulse invariance.Design of digital Butterworthfilter using the bilinear trans-formation. Comparison of theresulting designs.


Design of FIR Digital FiltersDesign of FIR filters usingwindows. Comparison of rectangular,Bartlett and Hamming windows.Frequency sampling method of filterdesign. Optimum equiripple FIRfilters.

39-min. Color Videotape. 22-0117 Purchase $325 Rental $33.

Computation of the DiscreteFourier Transform (1)Direct computation of the discreteFourier transform. Computationresulting from successive decimationof the sequences. The decimation-in-time form of the fast Fouriertransform (FFT) algorithm. Basicbutterfly computation.


Computation of the DiscreteFourier Transform (2)Interpretation of FFT flow graphfor in-place computation. Bit-reversed data ordering. Otherdecimation-in-time FFT algorithmsby rearrangement of the flow-graph. Decimation-in-frequencyFFT algorithm.


Computation of the DiscreteFourier Transform (3)Rearrangements of the basicdecimation-in-frequencyalgorithm. Relation betweendecimation-in-time and decimation -in- frequency through the trans-position theorem. Arbitraryradix FFT algorithms.


40 41

EconomicsRobert S. Pindyck

Economics is a subject thatconfronts us every day -- whetherwe like it or not. Nationalpolitics, for example, are intertwined with issues of economicpolicy: Should the federalbudget contain a deficit or asurplus and should the FederalReserve expand or contract themoney supply? How can thegovernment deal with problems ofinflation and unemployment? Theseare problems in macroeconomics.

But, pick up a newspaper and youwill be confronted with micro-economic issues as well. Shouldthe government tighten its

AM.

regulation of particular indus-tries? Why do shortages of oil,gasoline, or various foodstuffsoccur? These questions canbetter be understood by one whois familiar with the behaviorof consumers, firms, and individualmarkets.

No previous study of economicsis assumed, but a student witha working knowledge of differentialcalculus will get the most out ofthis approach to the material.

Robert S. Pindyck is AssociateProfessor of Management at MIT.

42

Economics

Economics

MicroeconomicsTwelve ColorVideotapes

Introduction to the EconomicProblemProduction and Exchange in aSmall Commune Economy. Introduc-tion to Production Functions,Production-Possibility Frontiers,and Supply and Demand.


Theory of DemandIntroduction to Consumer Demand.The Notion of "Utility". UtilityMaximization Subject to a BudgetConstraint. Introduction to In-difference Curves, and the DemandCurve of the Individual Consumer.


Consumer Theory and DemandBehavior of the Demand Curve ofthe Individual Consumer UnderChanging Prices and Income. TheMarket Demand Curve. Elastici-ties.


Market Supply and Demand (1)Introduction to Supply and Demand.Use of Supply-Demand Analysis toSolve a Variety of Economic Prob-lems. Shifts in Demand. Analyz-ing the Incidence of a Tax.


Market Supply and Demand (2)Price Regulation. Price Supportsand Subsidies. The Concept ofConsumer and Producer Surplus,and Its Application to the Evalu-ation of Government RegulatoryPolicies.


Production, Cost, and Theoryof the Firm (1)The Theory of the Firm. Internaland External Costs. Productionand Cost Minimization. The Cal-culation of Cost Functions.


Production, Cost, and Theoryof the Fimn-÷2)Short Run and_Long Run CostCurves. Marginal and AverageCosts. Marginal and AverageRevenues. How the Firm MaximizesProfits.


Introduction to Market StructurePure CompetitionBehavior of Competitive Firms.The Demand Curve as Seen by anIndividual Competitive Firm. TheSupply Curve of a Single Competi-tive Industry. Equilibrium ofthe Purely Competitive Firm andIndustry.


4243

MonopolyB avior of Monopolies. ProfitMaximization by a Monopoly.Government Regulation of a Monop-oly. Taxing a Monopoly.


Topics in Microeconomics (1)The Structure of American Indus-try. Monopoly, Oligopoly, andImperfect Competition. MeasuringMonopoly Power. Monopsony andOligopsony.


Topics in Microeconomics (2)Factor Demand and Factor Pricing.Market Structure and AmericanIndustry. The Performande ofAmerican Industry.


Group Discussion on Micro-economicskound-Table Questions andDiscussion.


MICROECONOMICS - Complete Set

Color Videotapes

Complete set of twelveColor Videotapes.


Suggested Text

No textbook is required forthis subject, but Economics byPaul A. Samuelson, (McGraw-Hill) is recommended for studentswho want an alternative treatmentof the subject matter. 917 pp.


MacroeconomicsTen Colorvideotapes

Introduction - Gross NationalProduct and IncomeIntroduction to Macroeconomics.Gross National Product andNational Income. National In-come Accounting in the UnitedStates.


Aggregate Demand (1)The Behavior of Aggregate Con-sumption. Aggregate Demand.Disposable Income, Consumption,Savings, and Government Spending.Introduction to the Multiplier.

46-min. Color Videotape20-0202 Purchase $360 Rental $36,

Aggregate Demand (2)Taxes and the Balanced BudgetMultiplier. Deficit Spendingand Fiscal Policy. The Useof Fiscal Policy to Controlthe Economy.


Study Guide

Summaries, reproductions ofoverhead transparencies,problems, problem solutions,final exam, and exam solutions.268 pp. (One per studentrecommended.)


A Complete Self -Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide.

4443

MACROECONOMICS - Continued

Interest Rates and InvestmentInvestment Behavior in theUnited States. Interest Ratesand Investment Demand. TheNotion of Present DiscountedValue, and its Application toBond Pricing.


Money and Commercial BankingThe Notion of "Money".The Operation of CommercialBanks. Commercial Banking andMoney Creation.

42-min Color Videotape20-0205 Purchase $340 Rental $34.

Federal Reserve SystemThe Structure and Operation ofthe Federal Reserve System.How the Federal Reserve SystemControls the Money Supply.


Demand and Supply of MoneyThe Demand for Money in The U.S.Economy. Equilibrium of MoneyDemand and Supply.


MACROECONOMICS - Complete Set

Color Videotapes

Complete set of of tenColor Videotapes

20-1200 Purchase $3245-(SAVE $445)50 Day Rental $338 (SAVE $33)

Suggested Text

No textbook is required forthis subject, but Economics byPaul ,A. Samuelson, (McGraw-Rill) is recommended for studentswho want an alternative treatmentof the subject matter. 917 pp.


Integration of Monetary andFiscal PolicyThe Integration of Monetary anaFiscal Policy. Introduction toand Use of the IS-LM Apparatus.Monetary and Fiscal Multipliers.The Use of Monetary and FiscalPolicy for Economic Stabilization.


Excess Demand and InflationExcess Demand and Inflation.Unemployment. The Inflation-Unemployment Trade Off. Issuesin Macroeconomic Policy.

57-min. Color Videotape20 -0209 Purchase $390 Rental $39.

Group Discussion on MacroeconomicsRound-Table Questions andDiscussion.


Study Guide

Summaries, reproductions ofoverhead transparencies,problems, problem solutions,final exam, and exam solutions.152 pp. (One per studentrecommended.)


A Complete Self-Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide.

444 5

Engineering EconomySanford B. Thayer

Engineering Economy in concernedwith the economic analysis ofinvestment alternatives. Fre-quently, there are severaltechnically feasible alternativeswhich will satisfy the functionalrequirements of the task. Butonly one of these is the mosteconomically attractive alterna-tive.

A study of Engineering Economyprovides students with the con-zepts and methodology necessaryto evaluate the impacts ofinterest rates, income taxes, andtiming of cash flows on the

economic attractivenesss ofinvestment proposals.

Many of the topics covered willalready be familiar from everydaycontact and no mathematicsbeyond simple arithmetic is used.

Sanford B. Thayer is Associate,Professor of Mechanical Engineeringat Colorado State University.These materials were prepared atCSU and are offered by MIT aspart of a cooperative effort ineducation.

46

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45

Engineering EconomyTen ColorVideotapes

Introduction to Engineering EconomyProvides an overview of the courseand introduces the concept of"Time Value of Money."


Uniform Annual Cash Flow MethodIntroduces the evaluation methodwhich converts all cash flows toa time adjusted equivalent annualamount. The example problem isthe economic evaluation of solarenergy for residential heating.


Breakeven AnalysisIntroduces the concept of break-even to find the point whereinvestments are equally attractive.The example problem is the break-even point of natural gas to makesolar energy economically attrac-tive for Solar House I atColorado State University.


ENGINEERING ECONOMY - Complete Set

Color Videotapes

Complete set of tenColor Videotapes.


Suggested Text

"Principles of EngineeringEconomy," by E.Grant andW.Iresonv Ronald Press, 1970,640 pp.


Present Worth MethodIntroduces the evaluation methodwhich converts all cash flows toan equivalent amount today. Theexample problem is present valueof a U.S. Treasury Bond.


Rate of Return MethodIntroduces the evaluation methodwhich solves for the prospectiverate of return on investedcapital. The example problemutilizes a share of AmericanTelephone and Telegraph Compar-common stock as the basis ofanalysis.


Benefit/Cost MethodIntroduces the engineeringeconomy method used by Federal,State, and local governments.The example problem is theBenefit/Cost analysis of theroute for Interstate Highway 70,near Vail, Colorado.


Study Guide

Comments, reproductions of allgraphics, reading assignments,problems, and problem solutions.250 pp. (One per studentrecommended.)

23-2100 Purchase $11.00 each.(104 Discount on five or more.)

A Complete Self-Study Subject.The set of videotapes describedabove can be used as a coorpiete seif-study subject when accaspanied bythe Study Guide and Suggested Text.

46 47

Cost-Effectiveness MethodIntroduces a method of analysiswhich allows alternatives to becompared on the basis of costsand criteria that cannot neces-sarily be expressed in monetary,terms. The example problemutilizes an economic evaluationof solar energy to produceelectrical energy.


Effects of Income TaxesIntroduces the effects of incometaxes on engineering economydecisions. The example problemutilizes an evaluation of theeconomic attractiveness of de-veloping a minimg site comparedto selling a lease.


'Replacement Studies"Introduces the illtilodology neces-sary to calculate the economctimc to replace an asset thatstill has a remaining physicallife. The example problem uti-lizes the replacement of anautomobile.


Sources of FundsThe lesson describes the commonsources of funds to finance in-vestment projects. The exampleproblem examines the financialstatements of a corporation.


47

48

Friction, Wearand LubricationErnest Rabinowicz

Friction, Wear and Lubricationis a coherent, up-to-date surveyof modern knowledge in thisimportant area. Industry sufferstremendous losses each year becauseof inefficient practices andignorance in overcoming frictionand wear problems. And it isthe aim of this series to providequantitative information thatwill be directly applicable tosolving these problems.

The major topics covered includethe various forms of wear, theircharacteristics and, magnitudes,

48

49

friction and its laws, the roleof lubricants, and such diverserelated topics as hardness,surface energy, polishing, andtroubleshooting.

The only background required forfull appreciation of theselectures and demonstrations is afirst-year course in materialsand in mathematics.

Ernest Rabinowicz is Professorof Mechanical Engineering at MIT.

7.

wrr

Friction, Wearand Lubrication

Twelve CoZorVideotapes

TribologyThe various topics that con-stitute the field of tribologyand their interrelation. Thetechnical literature. The con-cept of material hardness andits influence on the area ofcontact of surfaces.


WearWear, its definition, its placeboth as a cause of loss of use-fulness and a process with manyuses. History of wear and des-cription of the various typesof wear. Discussion of thesurface energy of solids and theenergy of adhesion of contactingsurfaces.


Adhesive WearPresentation of the Archardformulation of the law ofadhesive wear, and discussionof earlier work. Extensions andalternative formulations ofArchard's equation. Evaluationof steps to be taken to reduceadhesive wear.


Adhesive Particle SizeDerivation of the equations forthe size of particles generatedin adhesive wear. Experimentalconfirmation. Influence ofparticle sizes with respectto surface roughness of slidingsurfaces, and importance indetermining minimum clearanceof bearings.


. Abrasive WearDerivation of the equation forabrasive wear, and of com-plications which modify it.Evaluation of abrasive grainand of abrasion-resistant sur-faces. Remedies for avoidingor minimizing abrasive wear.


Corrosive WearCorrosive wear and itscharacteristics. Possiblebenefits if corrosion product isa lubricant. The causes offretting and the quantitativelaws governing material lossduring fretting. The mechanismof polishing and of burnishing.


Surface Fatigue WearThe mechanism of surface fatiguewear and the laws governing it.Discussion of the Weibull dis-tribution, its characteristicsand uses. Erosive wear and itslaws. The phenomena of frettingfatigue and its effect in re-ducing strength of structuralmembers.


FrictionThe history of friction, withemphasis on the roughness vs.adhesion controversy. The lawsof friction and the extent towhich they are obeyed. Frictioncoefficient values and how theyare measured. The magnitude offriction-induced temperature in-creases.


50 49

FRICTION, WEAR, and LUBRICATION - Continued

Stick-SlipThe relaxation and harmonic formsof frictional oscillations andhow they arise. Conditions forstick-slip and their relation tomaterial properties. Methods ofpreventing frictional oscil-lations. Uses of stick-slip.


Lubrication (1)Fluid lubrication, boundarylubrication, and the types oflubrication in between.Lubricants which form coherentfilms, and those that reduce thesurface energy. Characteristicsof solid lubricant film.


Lubrication (2)Effect of reduction of surfaceenergy on wear, and types oflubricants which are effectivein this regard. Petroleumlubricants, synthetic lubricants,E. P. agents and their pro-perties. Automotive lubricantsand additives.


TroubleshootingSystematic procedure fortroubleshooting, includingdetermining the characteristicsand function of the failedpart; examination bf itssliding surface; and com-putation of wear coefficient,temperature rise, and wearparticle size. Role of thelaboratory test in confirminga diagnosis. Some commontribological problems andmethods of curing them.


FRICTION, WEAR AND LUBRICATION - Complete Set

Color Videotapes

Complete set of twelveColor Videotapes


Suggested Text

Friction and Wear of Materialsby Ernest Rabinowicz, John Wileyand. Sons, 1965. 244 pp.

18-3100 Purchase $15.95 each

Study Guide

Photographs, comments, readingassignments, problems, problemsolutions, and final exam.244 pp. (One per studentrecommended)


A Complete Self-Study Subeat.The set of videotapes describedabove can be used ae a catripiets self-study itubjectiohen acoanpaniord bythe Study Guide, and! Suggested Text.

50 51

Introduction toExperimentationErnest Rabinowicz

An Introduction to Experimentationis a very practical series of lec-tures and demonstrations on thedesigning, carrying out, and re-porting of experiments. Thetopics covered include thecharacteristics of instruments,errors of measurement, statisticalanalysis of data, plottingfunctional relationships, cor-relation, and technical reporting.

This systematic approach to mena-ingful experimentation can beapplied with great benefit to awide variety of problems inresearch and engineering.

52

Experimentation has been taughtfor some years at MIT as atechnical discipline in its ownright.

The mathematical level of thisseries is not very high; someuse is made of calculus inderiving equations, but these canbe safely ignored by anyone moreinterested in application thantheory.

Ernest Rabinowicz is Professorof Mechanical Engineering at MIT.

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51 .

Introduction toExperimentation

Fourteen B&W 16wFilms or Videotapes

ExperimentationThe various steps in an experi-mental investigation. The his-tory of experimentation. Thehuman senses, their uses, andhow they are augmented bymeasuring instruments. Proper-ties of instruments.


Resolution of InstrumentsDiscussion of sensitivity,accuracy and resolution. Appli-cation to the problem of meas-suring foil thickness. Reso-lution of the microscope. in thefocal plane and in depth.Sensitivity and resolution ofthe chemical balance.


Errors of MeasurementErrors of the caliper micro-meter and how they can be mini-mized. Errors of the movingcoil galvanometer and theirindividual characteristics.Differences between random andsystematic errors, unit andproportional errors. Reductionof errors of measurement bybalancing or by partial balanc-ing.


Combination of ErrorsDerivation of formula for ex-ternal error propagation wherequantities are multiplied to-gether. Analogy with aimingat a target. Correspondingformula where quantities areridded or subtracted. Formulaeapplied to a caliper micrometerand a speedometer.


The Normal DistributionDeviation of the error compo-nents for an external error esti-mate. Error combinations pro-ducing distributions of measure-ments about the mean. The nor-mal distribution and conditionsunder which it arises. Uses ofthe normal distribution to esti-mate extreme values, and toeliminate data.


Internal Error EstimateImplications of a non-normaldistribution and ways of adjust-ing it to normalcy. The errorof the mean of a normal distri-bution (standard error) and itsmagnitude. Formula for internalerror.


Computing the Standard DeviationComparison of internal and ex-ternal error, and the optimumway of combining them. Systema-tic errors in measuring thevelocity of light. Definitionsof precision and of accuracy.Method of computing the standarddeviation a outlined, both whennumber of data points is smalland when it is large.


The y2 (Chi-Squared) TestThe x2 parameter defined, andadjustment for expended degreesof freedom explained. Use ofX2 in analysing coin tossingexperiments, a normal distribu-tion, and the classic experi-ments of Mendel.


52

53

The Poisson DistributionApplication of the x2 tests toshow personal error in esti-mating final digits. Derivationof the Poisson distribution andexplanation of its properties.Application of the Poisson dis-tribution to the utilization ofmaternity hospitals.


The Best Straight LineMethods of deriving the beststraight line through a set ofpoints. Discussion of the leastsquare method, with specialreference to problems arisingwhen the x measurements havesubstantial error.


Plotting Other FunctionsResolving choices when a numberof plotted functions will give alinear plot. Problem illustratedby plot of track records. Dis-cussion of methods of plottingthe exponential function.


INTRODUCTION TO EXPERIMENTATION -

Pilms/Videotapes

Complete set of fourteen B&W16 mm films or videotapes.


Suggested Text

An Introduction to Experimentationby E. Rabinowicz, Addison-Wesley,1970, 124 pp.411

15-3100 Purche $4.95 each.

CorrelationProcedures for detecting non-linearity. Plotting a non-linear function. Correlation,rank correion, and their use.Erroneous rdWults arising fromclassification,procedures.


The Technical Report (1)Principle laid down that techni-cal report is main method ofconveying experimental results,and that title and abstract aresorting devices. Description ofthe various sections of the re-port, and comments on do's anddon'ts in connection with them.


The Technical Report (2)Discussion of satisfactorygraphing methods. Peculiarconventions surrounding techni-cal reports - data and picturesare the best, narration has beentidied up.. Unacceptabld dis-tortions of the technical report- bad data edited out, unconven-tional ideas suppressed, deli-berate falsification.


Complete Set

Study Guide

Photographs, comments, readingassignments, problems, problemsolutions, and final exam.238 pp. (One per studentrecommended.)


A Complete Self-Study Abject.The set eines/Videotapes describedabove can be used as a complete self -study subject when accompaniedthe Study Guide and'Aggested Texbyt.

53

Mechanics ofPolymer ProcessingJ. R. A. Pearson

Mechanics of Polymer Processinganalyzes the mechanical behaviorof polymer melts. Processingtechniques for these melts haveemerged largely on an empiricalbasis, because their behavior hasnot been easy to describe. Thechemistry and physics of theseplastics and elastomers has becomeincreasingly well understood.But their most unusual propertiesare mechanical , and these vary'neatly -- with material, withtemperature, and with type ofdeformation.

55

The introductory lectures anddemonstrations in this seriesdescribe the structure andproperties of polymers andillustrate some of the importantprocessing techniques. Laterlectures concentrate on thefundamental mechanics of visco-elastic materials in terms ofmathematical models and theapplication of these ideas topolymer processes.

J. R. A. Pearson is Professor ofChemical Engineering at ImperialCollege, University of London.

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t

Mechanics ofPolymer Processing

IntroductionEight ColorVideotapes

Materials; Basic ProcessesCommon commercial polymers bychemical struture; hard or soft,cross-linked or thermoplastic.Geometric variations inproducts. Thermoplastic pro-cessing. Levels of knowledge;molecular, microscopic, con-tinuum.


Physical Properties of PolymersMolecular concepts: long chains,straight or'branched; sidegroups; copolymers.Statistical descriptions.Crystalline state. Glassy state.Rubbery state. Liquid state.Transitions. Supermoleculareffects.


INTRODUCTION - Complete Set

Color Videotapes

Complete set of eightColor Videotapes


Suggested Text

Mechanical Principles ofPolymer Melt Processing byJ.R.A. Pearson, MIT,1975, 148 pp.


Screw Extrusion of Pipe; In-jection MoldingThe screw extruder. Continuousoperation. Internal mechanismfor melting, mixing, pumping.Pipe extrusion through die. Ascrew pre-plasticized injectionmolding machine. Cyclicoperation. Flow and cooling inmold.


Film Blowing; Blow Molding;Thermoforming; Two-Roll MillingBiaxial extension of sheet infilm blowing. Transientfluctuation in continuous pro-cess. Extrusion for blowmolding. Cyclic operation ofblow mold. Thermal cycle inthermoforming; plunger, vacuumor pressure assisted. Mixingand blending in 2-roll mill.The rolling bank.


Study Guide

Comments, photographs, repro-ductions of overhead trans-parencies, reading assignments,problems, and solutions., 62 pp.(One per student recommended.)

21-2100 Purchase $4.00 each(10% Discount on five or more,)

A Complete Self -Study Subject.The set of videotapes dmgcribedabove can be amiss a complete self-study subject when accompanied by theStudy Guide and Suggested Text.

55

5 6

INTRODUCTION Continued

Kinematics of Flow ProcessesSteady and unsteady flows. Con-fined and free flows. Simpleshear flow. Lubricationapproximation. Extensionalflows, uniaxial and biaxial.


Mathematical Models for FlowProcessesFundamental laws. Fieldvariables. Approximations.Rheological equations of state.Uniaxial extensional flowdynamics. Steady simple sheardynamics.


Stability of Flow ProcessesNon-uniform and unstable flow.Time and space fluctuations.Tube and channel flowinstabilities; entry, exit andparallel flow effects. Sheetdrawing instability.


Control and Design of FlowProcessesControl of existing processes.Shape and property fluctuations.Control variables. Filmblowing as example. Surging in

. extruders. Die design. Needfor fundamental information.Quality control. The designprocess. Cost criterion.


Fundamentals ofPolymer Melt Mechanics

Twelve ColorVideotapes

General Rheological PropertiesDescription of solid, fluid,viscoelastic solid, elastico-viscous liquid; types ofuniform deformation; simpleone-dimensional models.

49-min. Color Videotape21-0201 Purchase $370 Rental,$37.

Continuum Approach. Stress &DeformationOrthogonal coordinate systems;the nature of stress - a tensor;displacement and deformation

the strain, rate-of-strainand vorticity tensors.


Conservation Laws & ConstitutiveRelationsConservation of mass, momentumand energy; rheologicalequations of state: elastic,viscous, viscoelastic.


Experimental InvestigationsDensity; specific heat;thermal conductivity. Extrusionand shear rheology. Experimentalresults for typical polymers.


Viscometric FlowSimple shear flow; the cone-and-plate viscometer; othermethods. Viscosity and normalstress differences.


Irrotational FlowsUniaxial extensional flow; pureshear flow; biaxial extensionalflow; extensional viscosity andother rheological functions.


56

Dynamic ViscosityComplex modulus; values forsimple models; time-temperaturesuperposition. Linear and non-linear viscoelastic models.


Unsteady FlowsDie swell; elastic recovery;melt fracture and flowinstability.


Basic Solution: ConfinedFlow (1)Pressure flow in uniformchannel; flow calculations forknown fluid; channel flow asrheological measurement.

41-miriColor Videotape21-0209 Purchase $335 Rental $34.

Basic Solution: ConfinedFlow (2)General uniform channel flowbetween parallel flat movingplates.


f

FUNDAMENTALS - Complete Set

Color Videotapes



Suggested Text

Mechanical Principles ofPolymer Melt Processing byJ.R.A, Pearson, MIT,1975. 148 pp.


The Lubrication ApproximationGeneral theory; simple exampleof wedge flow; applications.


Thin Sheet ApproximationsGeneral Theory; continuity andstress equilibrium equations;flat sheet flow; simple planeflow example; applications.


Application toPolymer Processing

Twelve ColorVideotapes

IntroductionObjectives of polymer processinggeometrical, physical and chemi-cal; control of process; impor-tance of thermal history; typesof process confined and freeflows.


Temperature Effects in ConfinedFlowsThe lubrication approximation;simple example of plane flow;dimensionless groups; scaletemperatures and process variables.


Study Guide

Comment4, PhotographOi 'repro-duCtione of overhead:transparencies, reading assignments,Problems, and OolutiOns0 112 PP.(00e per student reCommended.)

21 -2100 Purdhaie $5.00 eaCh.-(10% Discount on five or

A ComplateSelf-Study .5144,Wt.The set of videotapiae: dstiori.bedabove can be used as a comploted self-study subject whe$ accompanied by theStudy Guide and. Suggested TOrt.

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APPLICATIONS - Continued

Flow in DiesForms of extrudate; .symmetricalextrudates; quantitative analysis;use of dimensionless variables;simple example; instability indie flow.


Single Screw Extruder: MeteringZoneThe extruder overall; geometricalsimplifications; velocity profiles;dimensionless groups; approximatetheories; numerical solutions andcomputer programs.


Single Screw Extruder: MeltingZoneBasic models; the plug-pool modelwith its five zones solid bed,melt pool, swept melting layerand growing lubricating layers;mass and stress balances; surging.


Single Screw Extruder: FeedZone; Scale-upSolid plug models; complete modelfor plasticating extruders;scaling-up extruders.


APPLICATIONS - Complete Set

Color Videotapes


21-1300 Purchase $3840 (SAVE $575)sh 60 Day Rental $400 (SAVE $44)

Suggested Text

Mechanical principles of PolymerMelt Processing by J.R.A. Pearson,MIT.1975, 148 pp.


Fiber Spinning: GeneralOne dimensional model; conserva-tion equations; dimensionlessrepresentation and groups;steady-state equations; boundaryconditions.


Fiber Spinning: StabilityLinearized perturbation analysis;Fourier decomposition; sensitivityanalysis for various imposeddisturbances; stability analysisand draw resonance.


Film Blowing: Steady-StateSymmetricSteady axisymmetric flow;geometrical approximations;balance equations for mass, forceand energy; rheological relations;purely viscous model; extensions.


Study Guide

Step-by-step path through thematerial with summaries of thelectures, photographs, problemsand problem solutions. 108 pp.(One per student recommended.)



58

59

Film Blowing: Stability. FilmCastingLinearized analysis for sensiti-vity and stability of viscousfilm-blowing model; unsteadyaxisymmetric and steady non-axisymmetric disturbances.Kinematic model for film casting;growth of edge bead; linearizedsensitivity and stability analysis.

'48-min. Color Videotape21-0310 Purchase $365 Rental $36.

CalenderingNarrow channel approximation;simple plane flow equations;difficulty in specifying inletand exit boundary conditions;mixing; load on rolls; instability.


Injection MoldingGeneral remarks on process; flowin molds - unsteady and highpressure drop; simple exampleof disc mold; flow equations;freezing; complexity ofrheological forces involvingsimple shear and irrotationaldistortion; instability of flow.


59

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4,

Modern ControlTheoryMichael Athans

Modern Control Theory is anengineering discipline which dealswith specific analytical andalgorithmic methods which can beused to control complex stochasticdynamic systems so as to optimizetheir performance. These toolshave found wide applicability inaerospace and defense systems,industrial control systems,transportation systems, biologicalsystems, power systems, and socio-economic systems.

In addition to the theory, a setof computer subroutines has been

ay

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6o*04110'

V.

developed to analyze an importantclass of practical problems and todesign' suitable control systems.The basic pre-requisite for theselectures and demonstrations is aworking knowledge of vectors andmatrices and their operations aswell as an exposure to the notionof eigenvalues and eigenvectors.

Michael Athans is Professor ofElectrical Engineering andComputer Science at MIT andDirector of the ElectronicSystems Laboratory.

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%TS

Modern ControlTheory

System AnalysisEleven ColorVideotapes

Introduction to Optimal Controland Estimation Methods (1)Overview of philosophy of moderncontrol. Definition of deter-ministic optimal control,stochastic estimation, andstochastic control.


Introduction to Optimal Controland Estimation Methods (2)Block diagram description of finalengineering design using themethods of modei-n control theory.


SYSTEM ANALYSIS - Complete Set

Color Videotapes

Complete set of elevenColor Videotapes.

19-1100 Purchase $3295 (SAVE $450)55 Day Rental.$342 (SAVE $34)

Suggested Text

Optimal Control, by M. Athansand P.L. Falb, McGraw-Hill,1966, 879 ,PP.


Cooler Manual

An especially written manual ofcomputer subroutines. 208 pp.


The General Notion of the Stateof a Dynamical SystemIntroduction of state variables inan input-output representation.Input-state-output description oflumped systems using vectordifferential or differenceequations.


Linear Continuous Time DynamicalSystemsSystems described by linear,constant or time-varying, vectordifferential equations. Solutionmethods; the state transitionmatrix and the matrix exponential.Forced and unforced solutions.


Computer Card Deck

Set of punched cards in Fortranfor implementing programsdescribed in Computer Manual.


Study Guide

Reproductions of overhead trans-parencies, comments, readings,problems and problem solutions.192 pp. (One per studentrecommended.)


A Complete Self-Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Computer Manual, andSuggested Text.

61

62

SYSTEM ANALYSIS - Continued

Dynamic Linearization forContinuous Time SystemsThe notion of a nominal trajectoryfor nonlinear systems. Pertur-bation methods and Taylor seriesexpansions for vector-valuednonlinearities. The lineardynamic perturbation model.


Discrete-Time Dynamical SystemsPerturbation and dynamic linear-ization methods for systems des-cribed by nonlinear vector dif-ference equations.


Linear Time Invariant DynamicalSystemsReview of eigenvalues andeigenvectors; their role in theexpression of solutions of lineardifferential and differenceequations. Definition of, andtests for, stability.


The Relation of Transfer Functionsand State Variable RepresentationsReview of Laplace transforms forscalars, vectors, and matrices.Techniques for obtaining thetransfer matrix and transferfunction from state space re-'presentations. Relationships ofpoles, zeros, and matrix eigenvalues.


From Transfer Functions to StateVariable RepresentationsSystematic techniques for trans-forming a transfer function todifferent state variable realiza-tions. Illustrations usinganalog computer diagrams.


Controllability and ObservabilityDefinitions and tests for control-lability and observability.Physical interpretation of thesefundamental concepts.


Computer Routines for LinearSystem AnalysisUse of computer subroutines forcalculating solutions of lineardynamic systems. A helicopterexample.


Deterministic Optimal ControlTen ColorVideotapes

General DiscussionMotivation for optimal controlproblems. Counterintuitiveexamples. Relevance of scalarvalued criteria for performance.


The Minimum Principle ofPontryagin: Continuous TimeCaseStatement of the Pontryaginminimum principle for differentformulations of optimal controlproblems.

49-min. Color Videotape19-0202 Purchase $370 Rental 7,37.

The Dynamic Programming AlgorithmDiscrete-time optimal controlproblems. The principle ofoptimality. Bellman's dynamicprogramming algorithm andits implementation.


The Minimum Principle: DiscreteTime CaseDiscrete optimal controlproblems and the associatedminimum principles for theirsolutions.

43-Min. Color Videotape19-0204 Purchase $345 Rental $35.

62

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The Steepest Descent MethodDescription of a "simple"digital computer algorithmto solve deterministic optimalcontrol problems.

84-min. Two Color Videotapes19-0205 Purchase $555 Rental $60.

Numerical Example: Solutionof a Minimum Fuel Problemin the Apollo ProjectIllustration of the steepestdescent method to solve anorbit transfer problem involvingthe Apollo SSV orbiter stage.

21-min. Color Videotape19-0206 Purchase $210 Rental $21..

Newton's MethodGeneral philosophy of the Newtonor quasilinearization method.Reduction of minimum principleequations to the two-point-boundary value problem, andtheir iterative solution usingNewton's method.


Minimum Principle vs DynamicProgrammingContrast from a technical andalgorithmic viewpoint of thetwo methods for solving optimalcontrol problems. Open-loopvs closed-loop optimal controls.


Deterministic OptimalLinear Feedback

Twenty-one CoZor

Videotapes

Motivation for the Linear-Quad-ratic ProblemDetailed motivation for usingquadratic performance criteriafor the optimal control of thelinearized perturbational dynam-ics about a nominal trajectoryassociated with a nonlinearsystem. The nature of the opti-mal linear-quadratic solution;state perturbation linear feed-back.


The Solution of the Linear-Quad-ratic ProblemStatement of the Linear-Quadraticproblem for both continuous anddiscrete time systems. Solutionmethods via Riccati equations.Summary of off-line and on-linecomputations.


DETERMINISTIC OPTIMAL CONTROL - Complete Set

Videotapes

Complete set of tenColor Videotapes.


Suggested Text

Optimal Control,by M. Athansand P.L. Falb, McGraw-Hill,1966, 879 pp.


Study Guide

Reproductions of overhead trans-parencies, comments, readings,problems and problem solutions.306 pp. (One per studentrecommended.)

19-.2200 Purchase $13.00 each.(10% Discount on five or more.)

A Complete SelP;Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, and Suggested Text.

63

6

DETERMINISTIC OPTIMAL LINEAR FEEDBACK - Continued

Motivation for the Steady-StateLinear-Quadratic ProblemStatic linearization; state-inputequilibria and their optimalcalculation. Formulation of theoptimal dynamic control problemusing linearized perturbationdynamics.

104-min. Three Color Videotapes19-0303 Purchase $885 Rental $89.

The Steady-State Linear-QuadraticProblem: Continuous-Time CaseProblem definition and the natureof the optimal solution via thealgebraic Riccati equation.Constant gain state variablefeedback designs and their guaran-teed stability.


The Steady-State Linear-QuadraticProblem: Discrete Time CaseThe optimal control of lineardiscrete-time systems withrespect to quadratic performanceindices over an infinite timehorizon. The discrete algebraicRiccati equation. Stabilityof the closed loop designs.


The Steady-State Linear-QuadraticProblem with DeterministicDisturbancesModeling of exogeneous distur-bances using uncontrollablestate variable motels. Solutionof the regulation problem.Influence of the disturbances inthe overall control structureand their decoupling in thecontrol system design.


Control of Helicopter at HoverProblem formulation and solutionfor the design of an autopilotto keep a helicopter at a desiredhovering condition. How toselect the performance index forphysical problems.

31.-min. Color Videotape19-0307 Purchase $280 Rental $28.

Programs: Helicopter ExampleUse of the computer subroutinesto solve for the optimal feed-back gain for a helicopterhovering problem.


DETERMINISTIC OPTIMAL LINEAR FEEDBACK - Complete Set

Color Videotapes

Complete set of twenty-oneColor Videotapes.


Suggested Text

_Optimal Control, by M. Athansand P. Falb, McGraw Hill, 1966,878 pp.


Computer Manual

An especially written manual ofcOmputer subroutines. 208. pp.


Computer.Card Deck

Set of punched cards in Fortranfor implementing programsdescribed in Computer. Manual.


Study Guide

A step-by-step path through thematerial with viewgraph re-productions, comments, exercises ,

and solutions. 305 pp. (Oneper student recommended.)

19-2300 Purchase $13.50 each.(10% Discount on five or more.)A Complete Self -Study &West.The set of videotapes describedabove can be used as a mompaete self-study subject when accompanied bythe Study Guide, Computer Manual andSuggested Text.

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65

The Steady-State Linear RegulatorProblem for Constant DisturbancesProper formulation of the opti-mization problem for the designof linear quadratic regulatorsin the presence of constantdisturbances. The need to incor-porate a penalty on the control .

rates in the cost functional.The existence of integrators inthe optimal feedback design.

70-min. Two Color Videotapes13 -0309 Purchase $465 Rental $47.

Design of Proportional-Deriva-tive-Integral Controllers forTracking Step InputsAppropriate formulation ofoptimal linear-quadratic designsthat can follow multivariablestep inputs with zero steady-state error. Realization usingstate integral feedback plusproportional and integral chan-nels on the vector error signals.


Asymptotic Behavior of Steady-State Linear-Quadratic Closed-Loop SystemsGeneral properties of optimallinear-quadratic designs on theweights in the cost functionalcharge; motion of the optimalclosed loop poles in the s-plane.Effect of minimum and non-minimum phase zeros.


Optimal Control of a Macro-economic Model of the U.S.Economy (1957-1962)An economic example of usingoptimal linear-quadratic optimalfeedback control strategies tocontrol, in different ways, amodel of the U.S. economydeveloped by R.S. Pindyck.


Air Traffic Control in the NearTerminal AreaA numerical example that illus-trates how the solution ofthree distinct optimizationproblems can be used to obtainoptimal path stretching androute control strategies to landaircraft under both normal andemergency conditions.

152-min. Three Color Videotapes19-0313 Purchase $1000 Rental $100.

Computer Routines for Determi-nistic Optimal Linear FeedbackUse of computer subroutines forcomputing the solution to thesteady-state linear-quadraticproblem. A helicopter example.


Stochastic EstimationTwenty ColorVideotapes

IntroductionDefinition of the stochasticestimation problem. Physicalproblems. Mathematical models.Colored and white noise models.


Review of Probabilistic ConceptsRandom variables; expected values,variances, covariances, andcorrelations. Joint and condi-tional probabilities, conditionalexpectations and covariances.Extension of concepts to vectorand matrix valued randomvariables.


Response of Linear Systems to

White Noise Inputs: DiscreteTime CaseDiscrete white noise. Open loopmean and covariance propagationfor systems described by vectordifference equations. Transientand steady behavior. Predictionand forecasting.


6; 65

STOCHASTIC ESTIMATION - Continued

Response of Linear Systems toWhite Noise Inputs: ContinuousTime CaseOpen-loop prediction and fore-casting for systems described bylinear vector differentialequations. Dynamic evolutionof means'and covariance matrices.Steady state considerations.


The Bayesian Approach toParameter. EstimationPrior and posterior information.Mathematical modeling of multi-variable static experiments.Bayes rule and the relation ofprior and posterior (conditional)probability density functions.Linear-gaussian estimationproblems. Formulas that deter-mine the updated means andcovariance matrices.


STOCHASTIC ESTIMATION - Complete Set

Color Videotapes

Complete set of twentyColor Videotapes.


Suggested Text

Applied Optimal Estimation byA. Gelb, MIT Press, 1974, 374 pp.


Computer Manual


19-4000 Purchase $9.00 each.(101 Discount on five or more.)

The Discrete-Time Kalman FilterFormulation of the state esti-mation problem for linear dis-crete-time dynamic systemsdescribed by stochastic vectordifference equations, givennoisy measurements of linearcombinations of state variables.The discrete Kalman filter;predict and, update formulas forthe conditional mean of thestate and covariance matrices.


Effect of Changing CovarianceMatrix of Measurement upon aKalman FilterA four dimensional numericalexample that illustratesdynamic evolution of errorcovariances as a function ofnumber of measurements and ofthe value of the measurementcovariance matrix.


Computer Card Deck



Lecture Notes

To be published. Write forprice and information.

,A Complete Self-StudY, Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Lecture Notes, Computer Manual.and Suggested Text.

66

6 7

The Continuous Time Kalman-BucyFilterDefinition of the stateestimation problem for stochasticdynamic systems described bylinear time-varying vectordifferential equations, givenlinear measurements of thestate variables in the presenceof additive measurement noise.The Kalman-Bucy filter; theRiccati equation for dynamicpropagation of the errorcovariance matrix.


The Steady-State Kalman-BucyFilter: Continuous Time CaseAsymptotic behavior of theKalman-Bucy filter under assump-tions of time-invariantdynamics and stationary noisestatistics. Stability proper-ties. The algebraic Riccatiequation.


Steady-State Programs:Helicopter ExampleDescription of the digital com-puter subroutines for solutionof steady-state Kalman-Bucyfiltering problems, and thestochastic simulation of theresulting system. An illustra-tive example using helicopterdynamics.


A Visualization of KalmanFilteringAn illustrative example usingcomputer generated graphics ofthe Kalman filter using a doublyhinged pendulum.


The Steady-State Kalman Filter:Discrete Time CaseAsymptotic behavior of thediscrete Kalman filter for time-invariant systems and stationarynoise statistics. Constant gainrealizations. Stabilityproperties.


Numerical Example: Estimationof positions, velocities, andaccelerationsA numerical example using con-stant acceleration inertialdynamics to illustrate thestructure and accuracy of theKalman-Bucy filter.


Numerical Example: SensorTradeoffsIllustration of using the Kalmanfiltering theory for decidingthe best sensor to use forfixed dynamics.


Suboptimal Nonlinear FilteringAlgorithms: Discrete-TimeDefinition of nonlinear estima-tion problem. Computationaldifficulties of optimal estima-tion algorithm. Suboptimalalgorithms: the extended Kalmanfilter. Real time - 'computationalrequirements.


Numerical Example: Estimationof position, velocity, andballistic parameter for avertical re-entering bodyNumerical example illustratinghow bias estimation errorsassociated with the use of anextended Kalman filter, can beremoved through the use of asecond order filter.


67

6 3

STOCHASTIC ESTIMATION - Continued

Computer Routines for LinearStochastic EstimationUse of computer routines todesign and simulate the steady-state Kalman-Bucy filter. Ahelicopter example.


Stochastic ControlSixteen ColorVideotapes

IntroductionOverview of stochastic controlproblem. Typical applicationareas. General discussion ofstochastic optimal controlproblems and of their solution.


The General ProblemPrecise formulation of optimalstochastic control problems fornonlinear dynamical systemsdescribed by discrete-timestochastic vector differenceequations'. Stochastic dynamicprogramming. Conditionalexpectations and the classicalinformation pattern. Compu-tational difficulties.

89-min. Two Color Videotapes19-0502 Purchase $59n Rental $59.

STOCHASTIC CONTROL - Complete Set

Color Videotapes

Complete set-of sixteenColor Videotapes.


Computer Manual



The Discrete-Time Linear-Quadratic-Gaussian (LQG) ProblemOptimal stochastic control forlinear time-varying stochasticsystems described by vectordifference equations and noisymeasurements. The Gaussianassumption. Quadratic criteria.The separation theorem. Theoptimal linear feedback compen-sator. Analysis of the optimalcost-to-go.


The :Continuous-Time Linear-Quadratic-Gaussian (LQ)'ProblemFormulation and solution of the-optimal stochastic controlproblem for linear time-varyingdynamic systems described bystochastic vector .differentialequations. Quadratic perfor-mance criteria. Gaussian ran-dom processes. The separationtheorem. The structure of theoptimal linear feedback dynamiccompensator. The control andfiltering matrix Riccatiequations.


Computer Card Deck



Lecture Notes

To be published. Write forprice and information.

A Complete Self-Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Lecture Notes and Computer Manual.

68

69

Numerical Example of LQG Designfor a Third Order ContinuousTime SystemThe numerical characterizationof the optimal LQG dynamiccompensator for a specificnumerical example.


Systematic Procedures andNumerical ExampleNumerical solution of a fourthorder continuous time LQGexample. Structure of resultingoptimal dynamic compensator.

38-min. Color Videotape19-0506 'Purchase $320 Rental $32.

Control of a Nonlinear SystemAbout Desired Time Varying .

Trajectory -,-----

Step-by-ste0 procedures for thesuboptimal st.ochastic.controlof nonlinear SyStems describedby stochastic vector differentialequations. The blending ofopen-loop optimal controls andLQG designed feedback compensa-tors.


The Steady State LQG Problem:Continuous Time CaseFormulation and solution of theoptimal stochastic control prob-lem for linear time-invariant'dynamic systems with respect toquadratic performance criteriaand with stationary Gaussiannoises. The linear time-invar-iant LQG feedback compensatorand the separation property ofthe closed loop poles. Rulesof thumb for design.


Steady State Theory ComputerPrograms: Helicopter ExampleDescription of the computersubroutines that solve andsimulate steady state LQG designs.Illustration using a helicopterexample.


Control of a Nonlinear Systemabout Desired Constant Equilib-riumStep-by-step procedures for thesuboptimal design of a controlsystem for maintaining a timeinvariant nonlinear dynamicsystem abolit a. desired constantinput-state equilibrium.

39-min. Color Vid'eotape19-0510 Purchase $325 Rental $33.

Optimal Control of the F-8AircraftVisualization of LQG based con-trol of the longitudinal dynam-ics of the F-8 aircraft, subjectto wind gusts, using computergenerated images.


Computer Routines for LinearStochastic ControlUse of computer routines todesign and simulate the steady-state stochastic regulatorusing the LQG approach.


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70

Network Analysisand DesignAram Budak

70

Network Analysis and Design inthe Frequency Domain is intendedfor circuit designers who want tolearn about modern operationalamplifiers. The first set oflectures and demonstrationsdevelops a number of useful circuitanalysis techniques and appliesthese to a large number of sampleproblems.

In the second set, RC-operationalamplifier circuits are discussed.Ideal and one-pole rolloff modelingof operational amplifiers are

,used to study the characteristicsof many practical circuits.

This course assumes knowledge ofLaplace transformation and funda-mentals of circuit theory.

Aram Budak is Professor of ElectricalEngineering at Colorado StateUniversity. These materials wereprepared at CSU and are offeredby MIT as part of a cooperativeeffort in education.'

71

Network Analysisand Design

The Frequency Domain,7-!ght Color

Videotapes

Useful Circuit AnalysisTechniques (1)Discussion and application ofthe principle of superposition.


Useful Circuit AnalysisTechniques (2)Determination of eqUivalentcircuits.


Dependent SourcesAnalysis techniques involvingdependent sources.


The System Function'Discussion of poles, zeros, andsystem functions.


THE FREQUENCY DOMAIN - Complete Set

dolor Videotapes

.Complete set of eightColor Vi&otapes.24-1100 Purchase $2290 (SAVE $255)40 Day Rental $238 (SAVE $18)

Suggested Text

Passive and Active Net0OrkAnalysis and Synthesis byA. Budak, Houghton Mifflin,1974, 733 pp.

24-3100 Purchase.$17..-95 each.

Ladder NetworksRC, RL, LC, and Parallel LadderStructures.


Natural and Forced ResponseDecomposition of the responseinto its natural and forcedcomponents. Demonstration ofthe two components of the res-ponse.

39-min. Color Videotape24-0106 Purchase $ 325 Rental $33.

Step and Sinusoidal-Steady-StateResponseCalculation of step. and sinusoidalresponse of networks.


Magnitude and PhaseDetermination and interpretationof magnitude and phase characteris-tics. Demonstration of responsenear complex poles and complex.zeros.


PG

Study. Guide

Comments, chalkboard photographs,reading assignments, problemsolutions. 65 pp. (One perstudent recommended.)


A COMplete Self -Study Subject,The set orvideotapes describedabove can be used as a complete self-:study subject when accompanied bythe Study Guide and Suggested Text.

71

72

The Operational AmplifierTwelz,e ColorVideotapes

The Ideal Operational AmplifierModeling of the ideal operationalamplifier.


Linear Applications (1)Analysis of inverting, non-inverting, difference, and otheramplifier circuits.


Linear Applications (2)Operational amplifier circuitsfor producing variable impedance,grounded current source, andbandpass filtering.


The One-Pole Rolloff ModelDiscussion of the one-pole rolloffmodel-


Frequency ResponseFrequency response of invertingand noninverting amplifiers.Demonstrations of the magnitudevs. frequency curves and themeasurement of the gain-bandwidthproduct.


BandwidthComparison of bandwidth for singleand multistage amplifier circuits.Demonstration of extension ofbandwidth with a capacitor.

34-min; Color Videotape24-0206 Purchase $300 Rental $30.

Step ResponseRelationship between pole positionand rise time. Demonstration oframp generator.


Output ImpedanceOutput equivalent circuit ofamplifiers. Demonstration of theoutput impedance vs. frequencycharacteristic.

41-min. Color Videotape24-0208 Purchase $335 Rental $34.'

THE OPERATIONAL AMPLIFIER - Complete Set

Color Videotapes



Suggested Text

Passive and Active NetworkAnalysis and Synthesis byA. Budak, Houghton Mifflin,1974, 733 pp.


Study Guide

Comments, chalkboard photographs,reading assignments, problemsolutions. 100 pp. (One perstudent recommended.)



72

Ideal and Actual Frequency ResponseBandwidth and rise-time improvementwith negative capacitance.Demonstration of the effect ofnegative capacitance.


Offset, Slewing, and Dynamic RangeDiscussion of limitations ofintegrated-circuit operationalamplifiers. Demonstration ofvoltage-and current-limitedresponse.


Nonlinear Applications (1)Operational amplifier circuitsusing the nonlinear model ofoperation. Demonstration of theresponse of the dead-zoneamplifier.


Nonlinear Applications (2)Applications involving diodes andoperational amplifier circuits.Demonstration of the characteris-tics of a fullwave rectifiercircuit.


73

Nonlinear VibrationsJacob P. Den Hartog

Nonlinear Vibrations describesvarious methods -- exact andapproximate, numerical andgraphical -- for dealing withvibrations in systems describedby nonlinear differentialequations. Although 95 per centof vibrational problems can beanalyzed with the aid of linearvibration theory, there is a .

baffling five per cent whichclearly cannot.

A d-c motor driven by a d-c genera-tor periodically reverses itself!A jet engine governor with acentrifugal pendulum vibrates to

74

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A

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destruction. These and manyother problems of great practicalimportance can only be understoodin terms of nonlinear vibrationtheory.

It is the purpose of this seriesto use the simplest possiblemathematics while keeping thephysical interpretation of themathematical model in sight withevery step.

Jacob P. Den Hartog is ProfessorEmeritus of Mechanical Engineeringat MIT.

75

Nonlinear Vibrationst3- thyy,7 B

1,=->o tapes

IntroductionDifferences between linear andnonlinear vibrating systems...application of various differen-tial equations...physical illus-trations of some simple syst-tems...review of literature...description of the phase-planemethod of solution.

36-min. B&W Videotape16-0101 Purchase $235 Rental $24.

The Phase-Plane MethodIllustrated application of thephase-plane method to simplelinear systems...undamped vi-brator...negative spring...damped vibrator...negativedamping...isoclinics...'cannibal' asymptotes.


Application of the Phase-PlaneMethodFree vibration with'Coulombdamping...simple pendulum withlarge angular motion...cylindri-cal phase plane.


Pendulum in a Rotating PlaneApplication of phase-planemethod to a simple pendulumrotating about a verticalcenter line in a verticalplane...effect of centrifugalforce on the oscillation.


The Van der Pol EquationDescription of a self-excitedsystem with damping dependentupon amplitude...reduction ofthe differential equation, bydimensional analysis, to itssimplest form...comparison ofthe Van der Pol number to theReynolds number.


Relaxation OscillationsSolutions of the Van der PolEquation by general phase-planemethod..''. determination of limit-amplitude by energy balance...case of large damping (large Vander Pol number)... approximatecalculation of steady statefrequency.


Periodic Reversal of Rotation ofa D.C. MotorPresentation of a constant speedD.C. series generator driving aseparately excited D.C. motor...explanation of periodic reversalof rotation of the D.C. motor onthe basis of the Van der PolEquation.


Forced Undampled Vibrator withNonlinear SpringSolution by means ofMartienssen's method...Martienssen's diagram...the'jump phenomenon'...introductionof damping effects by energybalance...stable and unstablebranches in the resonance dia-gram.


7675

NONLINEAR VIBRATIONS - Continued

Piece-Wise Linear SystemsForced vibration of undamped vi-brator with piece-wise linearsprings by Martienseen's method...systems with clearances andpreset springs.

33-min. B&W Videotape16-0109 Purchase $220.Rental $22.

Forced Vibrator with NonlinearDampingReplacement of nonlinear dampingby 'equivalent' linear dampingto equalize the work per cyclein each case...reduction to alinear case in which the 'equi-valent linear damping constant'is dependent on frequency andamplitude.


Exact Solutions, (1)

Undamped free vibration with non-linear spring,.. forced undampedvibration with piece-wise linearspring...comparison of latter re-sult with Martienseen's approxi-mation in Lesson 9.


Exact Solutions, (2)

Forced vibration with Coulombdamping...comparison of thisexact solution with the approxi-mation of Lesson 10.


NONLINEAR VIBRATIONS - Complete Set

Videotapes

Complete set of twenty-three B&Wvideotapes

16-1100 Purchase $4315 (SAVE $645)115 DayRental $455 (SAVE 53)

Suggested Text

Mechanical Vibrations, (FourthEdition) by J.P. Den Hartog,McGraw-Hill, 436 pp.

16-3100'Purchase $16.50 each.

The Sommerfeld Effect'Jump phenomenon' resulting froma highly damped rotor accel-erated through its critical'speed by the increase of voltageof the driving D.C. motor...idealization of the system andsolution by energy balance.


Tuned Centrifugal PendulumFrahm's Vibration Absorber asapplied to torsional vibrationin reciprocating engines...utilization of centrifugal forcefor required tuning followingtotational engine speed...(onlylecture on linear systems).


Nonlinear Centrifugal PendulumJump phenomenon observed on air-craft piston engine...idealiza-tion to a simple system...delib-erate de-tuning of pendulum forsmall angles in order to tune itfor large angles of swing...system of two coupled differen-tial equations, both highlynonlinear.

24 min. B&W Videotape16-0115 Purchase $165 Rental $20.

Study Guide

Comments, photographs, readingassignments, problems, andproblem solutions. 244 pp.(One per student recommended.)

16-2100 Purchase $10.50 each.(10% D±scount on five or more.)

A Complete Self -Study Subject.The set of videotapes describedabozje can be used as a complete self-study subject when aocampanied bythe Study Guide and Suggested Text.

76

7 7

Solution and InterpretationSolution of the preceding equa-tions by a modified Martienssenmethod giving a diagram fromwhich the jump phenomenon can beseen immediately...calculationof the critical angle showingthe impossibility of engineoperation with pendulum swing

. above 30 degrees.


Aircraft Jet Rotor with BallBearings with ClearancesReduction of system to a simplemodel...illustration of jumpphenomenon by another modifica-tion of Martienssen's method...avoidance of large amplituderesonances by proper detaildimensioning.


Method' of Krylov-BogoliubovPresentation of systems withsmall and moderate nonlineari-ties in the damping or thespring...derivation of the(approximate) result in thestandard manner.


Physical Interpretation of theK & B FormulasInterpretation on the basis ofenergy balance and Fourieranalysis of the nonlinearforce...fundamental force har-monic in phase with motion in-terpreted as a spring; cross-phase component furnishingdashpot effect.


Method of GalerkinOriginally proposed for staticsystems...later applied to dy-namics and particularly toslightly non-linear vibrations...all previously discussedapproximate methods shown to bespecial cases of Galerkin.


ApplicationsTreatment of the cubic springand the large swing pendulum bythe four approximate methods...comparison of the approximatemethods with the exact (phase-plane) procedure, proving theK & B approximation to be thebest of the four.


.4110

Modified Martienssen Method-Subharmonic ResonanceVariation of the simpleMartienssen method adapting itto the greater accuracy obtain-able bythe K & B or 'harmonicbalance' method...physical dis-cussion of subharmonic resonance.


Volterra's FishesBiological problem of populationfluctuation of two species offish dependent upon one another...dimensionless treatment ofthe equations...graphical solu-tion and physical interpretation.


78 77

Probability andRandom ProcessesHarry L. Van Trees

Probability is a post-calculusapproach to this important mathe-matical discipline. Even acursory survey of enijineering,for example, reveals the wide-spread applicability of probabi-lity theory. Such diverse fieldsas systems analysis, decisiontheory, statistics, automaticcontrol, modern management,and cybernetics all rely on aprobabilistic approach.

r

r

r

r

rrr

r

is* OW.

Random Processes is a follow-onto Probability and a pre-requisite to study in such areasas advanced communications andqueuing theory. Included arediscussions of three completelycharacterized processes - thePoisson, Markov, and Gaussianprocesses.

Harry L. Van Trees is Professorof Electrical Engineering at MIT.

1.1411%.4444.

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78

rf

Probability

Elementary Probability TheoryThirteen 134W lgmmFiZms or Videotapes

Introduction to ProbabilityThis lecture presents a fewexamples of cases where probabi-lity theory is applied. Itdiscusses the subject of relativefrequency and its relationshipto the idea of probability.Physical systems and mathematicalmodels.


Formulation of MathematicalModels (1)Formulation of mathematical modelsin probability theory. Dealswith the definition of a probabi-listic experiment and with thedefinition of an event. Threeexamples involving the tossing ofa coin or of dice. Representationof events on lines or in two-dimensional space.


Formulation of MathematicalModels (2)Continues discussion of formula-tion of mathematical models.Events are defined as a col-lection of sample points. Theidea of an event in continuoussample space is illustrated.

30-min B&W Film or Videotape12-0103 Purchase $205 Rental $21.

Elementary Set TheoryIntroduces basic ideas ofelementary set theory,. Definesand illustrates graphically theideas of equality, inclusion,union, intersection, complementa-rity, difference, null-sets, dis-joint sets, and partitioning.


Theorem ProvingIntroductory lecture on theoremproving. Proof of an "IF andonly IF" type of theorem. Proofby contradiction.


Probabilistic ModelsCovers the five basic axioms ofprobability theory. Illustrates

- those axioms through a cumberof examples. Shows..that, onceprobability assignments havebeen made which are consistantwith the five axioms, the proba-bilistic model of an experimentis always a legitimate one._


Proof by InductionContinuation of theorem proving.Illustrates in detail proof byinduction. Presents an exampleinvolving the two basic steps oftypical proof by induction.


Joint ProbabilityIdea of joint probability isintroduced through the use oftwo examples. Shows that jointprobabilities must obey theaxioms of probability theory.


Conditional Probability (1)First of two lectures on condi-tional probability. Illustrateshow probabilities change whenevents are conditioned by otherevents. Definition of condi-tional probability.


79

80

ELEMENTARY PROBABILITY THEORY - Continued

Conditional Probability (2)Continuation of the previouslecture on conditional probability.The lecture goes through a detailedexample on reliability to illustratethe ideas of conditional probabilityBayes rule is derived.


Conditional Probability: ADigital Communications ExampleConditional probability is il-lustrated through a digitalcomunications example. Cons-truction of sample space fromconditional probability as-sumptions or measurements.Application of probabilisticideas to the design of thesystem.


Statistical IndependenceThe fundamental concept of sta-tistical independence isdefined and its meaning is il-lustrated through a number ofexamples. The utility of thisconcept in probabilistic analysisis discussed briefly.


Product Spaces & StatisticallyIndependent ExperimentsExtends the concept of statisticalindependence. Construction ofproduct spaces from statisticallyindependent experimental, outcomes.Successive coin tosses.


Random VariablesSixteen B&W 16mmFilms or Videotapes

Random Variables ;1)Introduction to random variables.Probability distributions andprobability distribution func-tions are defined. Propertiesof probability distributionfianctions.

26 -min. B &W Film or Videotape12-0201 Purchase $175 Rental $20.

Random Variables. (2)Continuous random variables.Probability densitfunctionsand their properties. Exampleof a uniform random variable.


ELEMENTARY PROBABILITY THEORY - Complete Set

Study Guide

Introduction to the topics,summarization of key concepts,problems, and problem solutions.374 pp. (One per studentrecommended.)


Pretest

Mathematics pretest to determineprofiCiency in calculus conceptsand techniques used in Probabi-lity. 74 pp.


A Complete Self-Study Subject.The set of films/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Lecture Notes andSuggested Text.

Films/Videotapes

Complete set of thirteen B&W16 mill films or videotapes.


Suggested Text

Probability and Random Processes,W.B. Davenport, Jr., McGraw Hill,1970, 542 pp. ,


Lecture Notes

Chalkboard photographs of all thefilms/videotapes of Probability.


81

Canonical Random VariablesDescribes the standard variablesoften used in practice. Expo-nential random variable isintroduced and illustrated.


Mixed Random VariablesRandom Variables are classifiedas continuous, discrete or mixed.The definition of an impulse isprovided. Detailed example it --lustrates mixed random variables.

30"min. B&W Film or Videotape12-0204 Purchase $205 Rental $21.

ConditioningThe conditioning of randomvariables is defined. It isshown that conditional randomvariables have all the proper-ties of ordinary random variables.


Multiple Random Variables:DiscreteDefinition of joint probabilitydistribution functions. Defini-tion of marginal probabilitydistribution functions. Discus-sion of the properties of bothA detailed example is presented.

34-min. B&W Film or Videotape12 -0206 Purchase $225 Rental $23.

Continous Random VariablesJoint probability distributionfunctions for continuous randomvariables. Joint probabilitydensity functions, marginaldistribution functions, andmarginal density functions forcontinuous random variables.Properties and examples.


Impulsive DensitiesDensities containing impulses arediscussed. Integration anddifferentiation for these densitiesare illustrated.


Statistically-Independent RandomVariablesStatistical independence isdefined in terms of probabilitydistribution functions. Theconcept is illustrated with thederivation of a marginal densityfunction. The idea of utility isintroduced.


Conditioning by SetsThe conditioning of probabilitydistributions and probabilitydensities on sets is illustrated.Conditional distribution functionsare defined.


Point ConditioningConditioning is extended to point-conditioning. This leads to thedefinition of conditional distribu-tion functions of random variables.


A Digital CommunicationApplicationA detailed example of a com-munication system with noiseadded is presented. Model ofthe communication system and theidea of minimum error decision.Computation of error probabilities.


81

82

RANDOM VARIABLES - Continued

Functions of a Random VariableComputation of probability dis-tributions for functions of asingle random variable. Standardprocedure for this computation.Illustration through example.


Functions of Vector RandomVariables (1)Computation of probability dis-tributions for functions ofvectors of random variables.Standard procedure. Specialcase of statistically independentrandom variables.

19-min. B&W Film or Videotape12-0214 PUrchase $130 Rental $20.

Reliability APplicationsIntroduction to the computationof reliability. Standard con-fi uraV.ons of networks. Compo-nts in series and in parallel.

34 -min. B&W Film or Videotape12-0215 Purchase $205 Rental $21.

Function of Vector RandomVariables (2)More complicated derivations ofprobability distributions forfunctions.of vectors of randomvariables. Illustration throughexample.


RANDOM VARIABLES - Complete Set

Films/Videotapes

Complete set of sixteen B&W16 mm films or videotapes.

12-1200 Purchase $2310,(SAVE $255)80 Day Rental $308 (SAVE 1)

Suggested Text

Probability and Random Processes,W.B. Davenport, Jr., McGraw Hill,1970, 542 pp.


Lecture Notes.

Chalkboard photographs of all thefilms/Videotapes of Probability.


Statistical AveragesEleven B&W 16mmFilms or Videotapes

Statistical Averages: Expectationof a Random VariableThe rundamental concept ofexpectation is introduced. Com-putation of expected values forcontinuous and discrete randomvariables.


Expectations of Functions of aRandom VariableThe concept of expectation isextended to functions of randomvariables. It is shown thatexpectation is a ainear operator.Examples are presented.


Moments of a Random VariableMoments and central moments aredefined. Variance and standarddeviation. Properties ofvariance and examples.


Study Guide

Introduction to the topics,summarization of key concepts,problems, and problem solutions.542 pp. (One per student .

recommended.)

12-2200 Purchase $17.50 each.(10%.Discount on five or more.)

A Complete Self -Study Subject.The set offi.lms/Videotapes describedabove can be used as a complete self-study subject when accompanied bytheStudY GUideLecture Notes andSuggested Text.

82 8t3

The Chebyshev InequalityThe Chebyshev inequality isderived and explained. The lec-ture also includes a discussionof how good a Chebyshev inequalityis as a bound on probabilities.


Estimation of Random VariablesDeals with the choice ofestimators for random variables.The mean-square error is discus-

,

sed as a criterion for estimation.Two examples illustrate theconcept.


Conditional ExpectationThe idea of conditional expec-tation is introduced. Conditionalexpectation on a joint Gaussianprobability density. Importanceof the concept in estimation.


Minimum Mean-Square ErrorEstimationReviews the idea of the minimummean-square error estimator. Anexample involving the joint.Gaussianprobability density is presented.


STATISTICAL AVERAGES - Complete Set

Films/Videotapes

Complete set of eleven B&W16 mm films or videotapes.

12-1300 Purchase $1645.(SAVE $145)55 Day Rental $212 (SAVE $16)

Su1.ested Text

Pro,ability and Random Processes,W.B.\Davenport, sr., McGraw Bill;1970) 542 pp.

12- 00 Purchase $19.50 each.

Lecture Notes

Chalkboard photographs of all thefilms/videotapes of Probability.


Joint Moments: CorrelationJoint moments of random variablesare defined. Correlation,covariance and the correlationcoefficients. Basic propertiesof joint moments. Predictive value.


Linear EstimationLinear estimation is introduced.Fundamental expressions arederived. Minimum mean-squareestimators are discussed in thislight.


Characteristic FunctionsCharacteristic functions aredefined. Tile, four fundamentalproperties of characteristic func-.tions are derived.


Joint Characteristic FunctionsThe concept of a characteristicfunction is extended to vectors ofrandom variables. Properties ofjoint characteristic functions arederived and discussed.


Study Guide

Introduction to the topics,summarization of key concepts,problems, and problem solutions:406 pp., 40neqaer studentrecommended.)


A Complete Self- Study Subject.The set offiTSISiVideOtapes:describe4above can be used:de a Complete self-,Study subject when accompanied bythe Study Guide, Lecture 'Notes andSuggested Text.

84 83

Limit Theorems and StatisticsNine B.Wl&mmFiZr'w or Videotapes.

Sample Means and the Weak Lawof Large NumbersThe sample mean is presented asan estimator of expectation. Theweak law of large numbers.Convergence in the Mean-squaresense. Discussion of differenttypes of convergence.

30 min. B&W Film or Videotape12-0401 Purchase $205 Rental $21.

Relative FrequencyRelative frequency.is defined.Shows that the relative frequencyof an event converges to theprobability of that event. Anexample is presented.


The Gaussian ApproximationIntroduces the idea of using theGaussian approximation for largesamples. An example usingbinomial distribution is discus-sed in detail. Comparisonbetween exact estimates and theGaussian approximation.


Central Limit TheoremThe derivation of the centrallimit theorem is outlined. Itsimplications are discussed indetail. Illustration approxima-tions through the central limittheorem.


Introduction to StatisticalInferenceThe idea of statistical inferenceis introduced. Estimation of aprobability density, estimation ofmoments, hypothesis testing,testing with unspecifed alter-na tives. The meaning ofstatistics.


Estimation of the Moments of aRandom VariableEstimation of moments. Unbiasedestimators. Consistant estimators.Normalized variance. Illustrationthrough the use of two statisticalproblems.


LIMIT THEOREMS AND STATISTICS - Complete Set

Films/Videotapes

Complete set of nine B&W16 mm films or videotapes.


Suggested Text



Lecture Notes

Chalkboard photographs of all the-films/videotapes of Probability.

'12-4100 Purchase $4.50 each.

Study Guide

Introduction to the topics,summarization of key concepts,problems, and problem solutions.254 pp. (One per studentrecommended.)


A Complete Self-Study Subject.The set of films/videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide, Lecture Notes and.Suggested Text. .

84

Estimation of the Parameter of aProbability DensityProcedure and issues in theestimation of parameters ofprobability densities. Like-lihood functions. Maximum like-lihood estimators. Biases.


Performance Bounds: The Cramer-Rao InequalityThe Cramer-Rao inequality as alower bound on the variance ofunbiased estimators. Efficientestimators. Comments on tne useof efficient estimators.


Estimation of the ProbabilityDensity of a Random VariableDetailed example on the estimationof a probability density function.Pitfalls and procedures for theestimation of probabilitydensities. Use of varianceanalysis.


8(85

Random Processes

IntroductionSeven B&W

A VideotapesIntroduction to Random ProcessesIntroduces, through the use ofexamples, the analytical ap-proaches by 'which random processtheory may be applied to avariety of physical problems.


Random Processes: Basic Conceptsand DefinitionsExtends the usual sample-spacedefinition of random variables

. to the case of random processes,and thereby introduces thenotion of a complete character-ization.

28-min. B&W Videotape'13-0102 Purchase $190 Rental $20.

Fixed-Form Random ProcessesDiscusses the simple case offixed-form processes, whereina small number of randomvariables completely character-ize the process.

25-min. B&W Videotape13-0103 Purchase $I70-Rental $20.

INTRQDUCTION TO RANDOM PROCESSES -

Videotapes

Complete set of seven B &Wvideotapes.


Suggested Text


12-3100 Purchase-$19.50 each.

Binary Transmission WaveTreats the binary transmissionwave and introduces stationarityconcepts.


Random Telegraph WaveConsiders the random telegraphwave and uses that example tointroduce the minimum mean-square error (MMSE) predictionproblem.


Second-Moment CharacterizationsRelaxes the constraint of completecharacterization by introducingthe concept of partial character-ization by the mean function andcorrelation function.


The Role of the CovarianceFunction in EstimationReturns to the MMSE prediCtionproblem for the case in which thepredictor is constrained to belinear.


CompleteSet

Study Guide

A step -by -step path through thesubject with photoaraphs, problemsets, quiz, and 'solutions.164 pp. (One per studentrecommended.).


A Complete Saif- Study Subject.The set of videotapes describedabove can be used as a complete self-study subject when acconranieci bythe Study Guide and Suggested Text.

86

87

Linear SystemsTwelve B&WVideotapes

System DescriptionsIntroduces the basic concept of asingle-input single-output system,and presents a number of examplesand special cases including theimportant class of linear systems.


Linear System DescriptionsDiscusses the characterizationof a linear time-invariant (LTI)system in the time domain by itsimpulse response.


Measurement of Inpulse Response"Demonstration of the relativeinvariance of linear time-invariant system responses to thedetailed shape of a pulse inputof short duration but fixed area.


Convolution IntegralProvides calculational exerciseswith convolution integrals, i.e.the time domain input-outputequation for an LTI sytem.


LINEAR SYSTEMS - Complete Set

Videotapes

Complete set of twelve B&Wvideotapes.


Suggested Text,

Probability and Random,Processes,W.B. Davenport, Jr., McGraw Hill,1970, 542 pp.


System ClassificationProvides a further investigationof the classification of systemsaccording to their input-outputproperties.


Complex Exponential Inputs':Frequency Domain AnalysisBegins the frequency domainanalysis of LTI systems by consi-dering the response of suchsystems to complex exponentialexcitations.28-min. B&W Videotape13-0206 Purchase $190 Rental $20.

Periodic Inputs and Fourier SeriesContinues the frequency domainanalysis of LTI systems bydeveloping the Fourier seriesrepresentation for periodicsignals and corisidering the res-ponse of such systems to periodicinputs.

28-min. B&W Videotape13 -0207 Purchase $190 Rental $20.

Fourier Series DemonstrationApproximation representation ofa square wave by a sum of sineand cosine waves - even and oddfunctions, even and odd harmonics,Gibb's phonomenon, mean squareerror property.

15 min. B&W Videotape13-0208 Purchase $115 Rental $20.

Study Guide

A step-by step path through thesubject with. photographs,problemsets, quiz, and solutions.282 pp. (One per studentrecommended.)


A Complete Self-Study Subject.The set of videotapes *describedabove can be used as a complete self-study subject when accompanied bythe Study Guide and Suggested Text.

8887

LINEAR sYsrkms - Continued

Fourier TransformsMakes the transition from the:Fourier series to. the Fouriertransform representation foraperiodic signals, and derivesthe convolution - multiplicationtheorem that relates the timeand frequency domain representa-tions of LTI system input-outputpairs.

33-min. B&W Videotape:13-0209 Purchase $220 Rental $22.

System FunctionsDescribes some techniques formeasuring system functions(impulse response and frequencyresponse), and also considers theanalysis of linealE systemscharacterized by differentialequations. or the cascade ofseveral linear systems.

35-min. B&W Videotape13-0210 ,Purchase $230 Rental $23.

Fourier Transform PropertiesTreats the mathematical propertiesof the Fourier transform.

42-min. a&W Videotape.13-0211 Purchase $270 Rental $27.

-Sampling TheoremDiscusses the representation ofa bandlimited waveform by itstime samples.

28-min. B&W Videotape13-0212 Purchase $190 Rental-$20.

SECOND MOMENT THEORY - Complete Set

Videotapes

Complete set of eight B&Wvideotapes.


Suggested Text

Probability and Random Processes,W.B. Davenport, Jr., McGraw Hill,1970,.542 pp.

12-v3100 Purchase $19.50 each-

Second Moment TheoryEight*B&WVideotapes

Linear Systems with RandomProcess InputsBegins the study of linearfiltering of random processes byderiving the mean function andcorrelation function of the outputof a linear system driven by noise.


Time AveragesBuilds upon the results of theprevious lecture to investigatethe relationship between statistical(ensemble) averages and empirical(time) averages of random processes.


Frequency Domain Analysis ofStationary Random ProcessesDevelops the basic frequency -domain analysis of wide-sensestationary random processes.

36-min. B&W Videotape*13-0303 Purchase $235 Rental $24.

White NoiseDevoted to the definition and useof white-noise processes in linear-system calculations.


Study Guide

A step-dby step path through thesubject with photographk,roblemsets, quiz, and solutions.230 pp. (One per.studentrecommended.)

13-2300 Purchase $7.50 each.(10% Discountph five or more.)

A Complete Self-Stitdy Subject.The set of videotapes describedabove can be used as a complete self-study subject when accompanied bythe Study Guide and Suggested Text.

88

8 9

Two Applications of White-NoiseDiscusses two applications ofwhite noise: synthesis of arandom process with a desiredspectrum, and measurement Oflinear-system impulse response.


Matched FiltersDerives the matched-filter asthe optimum linear processor fordetection of a known signal inadditive white noise.


Optimum Fixed Form Linear FiltersContinues the discussion oflinear signal processing byconsidering optimum fixed-formfilters for estimating a randomsignal embedded in additiveenoise.

34-min. B&W Videotape13-0307 Purchase $225 Rental.$23.

Optimum Linear FiltersConcludes the discussion of linearsignal processing by deriving theoptimum unrealizable filter forestimating a random singalembedded in additive noise.


POISSON PROCESSES - Conyolete Set

Videotapes

Complete Set of five B&Wvideotapes.

13-1400 Purchase $815 (SAVE $70)25 Day Rental' $97 (SAVE $10)

Suggested'Text

Probability and Random Processes,'W.B. Davenport, Jr., McGraw Hill,1970, 542 pp.

12-3100 Purchase $19:50 each.

Poisson ProcessesFive B&WVideotapes

Introduction to Poisson ProcessesIntroduces the Poisson countingprocess through its independentincrements property and mentionsits potential application areas.


Poisson Counting ProcessesReviews the definition of thePoisson counting process andcalculates the counting probabi-lities from its incrementalstatistics.


Arrival TimesDerives the arrival-time statisticsfor the Poisson counting process.

14-Min. B&W Videotape13-0403 Purchase $100 Rental $20.

Filtered Poisson ProcessBuilds upon previous results tostudy the statistics of a linearlyfiltered Poisson impulse traini.e. a shot-noise process.

30-min. B&W"Videotape13-0404 Purchase $205 Rental $21.

Study Guide

A step-by-step path through thesubject wilih photographs problemsets, quiz, and solutions.118 pP. (One per studentrecommended.)

13-2400 Purdhase $4.00 each.(10% Discount on five or more.)

A Complete Self-Study Subject.The.set of videotapes describedabove can be used as a comptete self-study subject when accompanied bythe Study Guide and Suggested Text.

89

9.0

POISSON PROCESSES - Continued

Limiting Behavior of FilteredPoisson ProcessesContinues the development of shot-noise statistics by demonstratingthe approach of high-density shot-noise to a Gaussian distribution.


Markov ProcessesSix B&WVideotapes

Introduction to Markov ProcessesBegins the study of discrete-state continuous-time Markovprocesses by use of examples, andintroduces the state transitiondiagram.


Markov Process EquationsConsiders the basic analysistechniques for finding thetransient and equilibrium statisticsof a discrete-state continuous-time Markov process.


MARKOV PROCESSES - Complete Set'

Videotapes

Complete set of six B&Wvideotapes.


Finite-State ProcessesDiscusses explicit solutiontechniques for the transient andequilibrium behavior of finitestate Markov processes.


Pure Birth ProcessObtains the state-occupationprobabilities for a pure-birthprocess.


Linear Birth ProcessesContinues the discussion of theprevious lecture for the case oflinear birth processes.


Equilibrium Distributions:Infinite State ProcessesInvestigates-the existence ofand solution for the equilibriumdistribution in an infinite-state Markov process.


5.

Study Guide

A step-by-step path through thesubject with photographs, problemsets, quiz, and solutions.156 pp. (One per studentrecommended.)


A CompleftSaP.Stu4 Wrject.The set of videotapes describedabove can be used as a.complete self-study subject when accompanied bythe Stuck Guide.

90

91

Gaussian ProcessesSeven B &WVideote#)ec

Introduction to Gaussian RandomProcessesIntroduces the Gaussian processthrough examples that make use ofthe central limit theorem.'


Gaussian Random VectorsDevelops the properties ofGaussian random vectors includingjoint probability density, andcharacteristic functions.


Gaussian Random ProcessesDefines the-Gaussian'randomprocess in terms of Gaussianrandom vectors and uses thedefinition to show that the meanand covariance function completlydhAradteri2e-:!the,Gaus.s.i4n process.


GAUSSIAN PROCESSES - Complete Set

Videotapes

Complete set of seven B&Wvideotapes.

13-1600 Purchase $870 (SAVE $75),30 Day Rental $134 (SAVE $10)

Suggested Text



Gaussian Processes and LinearSystemsCombines the results of theprevious lecture with'-those ofsecond moment theory to completelycharacterize the output of a linearsystem driven by Gaussian noise.


Gaussian Processes and NonlinearSystemsUses the moment factoring, pro-perty of Gaussian random variablesto investigate the response ofnon-linear systems to Gaussian noise.


Linear Optimality and GeneralOptimalityUses the results of previouslectures in conjunction with theoptimum linear filtering resultsof second moment theory to showthat linear optimality is identi-cal to global optimality forGaussian processes

31-min. B&W Videotape13-0606 Purchase $210 Rent41 $21..

Summary of Gausian ProcessesConcludes the study of Gaussianprocesses by summarizing the keyproperties* derived in the previouslectures.


Study Guide

A step-by-step path through thesubject with photographs,problemsets, quiz, and solutions.

, 180-pp. (One: per studentrecommended.)

13 -2600 Purchase $6.00 each(10% Discount on five or more.)

A Complete Self Study Subject.The set of videotapes describedabove can be used as "a oompiete self-study subject when accompanied bythe Study Guide and Suggested Text.

91

Measurement ofProcess Characteristics

Three B&WVideotapes

Measurement of Random ProcessCharacteristicsIntroduces the goals of andproblems encountered inmeasuring the statistics of arandom process from sample-function observations.


Measurement of Mean-SquareValue of a Random ProcessEvaluates the bias and varianceof the time-average estimate ofthe mean-square value of aGaussian random process.


Measurement of'Power DensitySpectraProvides an introduction tospectral density estimation anddevelops an appreciation forthe tradeoff between resolutionand accuracy.


MEASUREMENT OF PROCESS CHARACTERISTICS - Complete Set

Videotapes

Complete aet of three B&Wvideotapes.


Suggested Text

Probability and Random Processes,W.B. Davenport, Jr., McGraw Hill,1970 542 pp.


r

Study Guide,

A Step.-by.-Step path through thesubject with photographs,problem sets, quiz,and solutiOns.solutions. 58 pp. (One perstudent recommended.)

13-2700 Purchase $4.00 eachJ10% Discount Oh five or.more.)

A CarpieteSetf-StudlySWVect.The set of videotapes deemilbect,above can be used as a complete eelfstuck subject when execontpanied bythe Study Guide and Suggested Text.

92

93

Thermostatics andThermodynamicsMyron Tribus

Thermostatics and Thermodynamics- An Information Theory Approachasks whether there is more thanan analogy between thermodynamicentropy and communication entropy.What is the connection betweenstatistical mechanics and thermo-dynamics? This series'of tenlectures develops probabilitytheory and entropy from an informa-tion theoretic basis. The resultsare applied to a variety ofproblems to build up the conceptsof statistical inference neededto establish statistical mechanicsand thermodynamics.

These color videotapes wererecorded in a television studiobefore a small group of practicingengineers. The series was pro-duced in Rochester, New York,under a grant from the XeroxCorporation.

Myron Tribus was Senior VicePresident, Xerox Corporationand is now Professor of Engineeringand Director, Center for AdvancedEngineering Study, MIT.

Ior

oak

AP--at/MEM

94

Thermostatics andThermodynamics

Ten ColorVideotapes

Entropy in Thermodynamics andCommunicationConstrasts inductive and deductivelogic. Gives desiderata for thedesign of an inductive logicsystem. Introduces the use ofBoolean symbols.


Logical Basis for ProbabilityConditional probability, scalingrules, functional constraints, thelogic of denial statements, allow-able transformations of probability.


A System of Inductive LogicReview of consequences of desider-ata for a. system of logic. Pro-bability as an "encoding" ofknowledge. How to combine Booleanand ordinary algebraic .operations.Historic interpretations of pro-bability; Bayes-equation andcommon sense.


Applying Bayes EquationBayes Equation applied to cancerdetection. Calibration vs use ofequipment. A method to "extendthe conversation." Using theevidence transformation and othertransformations.


Hypothesis Testing and SequentialTestingProbability function applied toBernoulli trials. The relationbetween probability and frequency.The evidence form of probabilityapplied to hypothesis testing andsequential testing in qualitycontrol.


Hypothesis TestingBayes Equation. The cancerproblem: should a biopsy beperformed? Hypothesis testing.The test of a random numbergenerator, the Chi SquareEntropy as a measure of un-certainty.


EntropyEntropy as a, measure .of ignorance.The maximum entropy principle.An application: predicting ordersize from order data. The Gibbs-Jaynes formalismof statisticalinference.


The Thermodynamics of a MythicalEconomyThermodynamics of Upper and LowerSlobovia (the "Thermodynamics" ofa mythical economy). The laws ofthermodynamics for a non-physicalsystem. The exponential distribu-tion and an analog of temperature.The concept of negative temper-ature. The grand canonicaldistribution for an artificialeconomy.


94

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Statistical ThermodynamicsStatistical Mechanics. TheBoltzrc-n distribution. The grandcanonical distribution.. The thirdlaw. The minimum postulatesrequired for thermophysics. Therelation between macroscopicconcepts of work, path, heat,reversibility, etc. and statis-tical parameters


Classical ThermodynamicsStatistical and classical thermo-dynamics compared. The basis forirreversibility in statisticalphenomena, the domain of appli-cability of thermostatics. Therole of diffusion in entropygeneration. Why does thermo-dynamics work? Review of the10 lectures.

53-min. Color Videotape29-0110 Purchase $380. Rental $38.

THERMODYNAMICS - Complete Set

Color Videotapes

Complete set of tenColor Videotapes

29-1100 Purchase $3305(SAVE$450)50 Day Rental $344 (SAVE 34)

95

90

Special Programs

Among the many lectures anddemonstrations listed earlier inthis catalog are a few that bearspecial mention. The purpose ofthis section is to single theseout as well as to introduce afew one-of-a-kind programsproduced by MIT. Thus, in thepages that follow, you will findlisted once again such outstandingdemonstrations as "Recursion" aswell as such unusual productions -

"Mt

96

listed for the first time - as"Women's Work: Engineering."

In addition,you.will find aspecial series on "The Managementof TechnologiOal Innovation"recorded in color in December1975. Most of the other.. lecturesand demonstrations were recordedin: the CAES color studio; the two"Women's Work" documentaries,however, were filmed on location.

4

9!

s.

Special Programs

Women's Work: EngineeringA documentary film designed tomotivate young women to considercareers in engineering. Showswomen engineering students andprofessional engineers in school,on the job and at leisure. Alsoconfronts the problem of com-bining a career with the res-ponsibilities of marriage andraising children.

26-min. 16 mm Color Film orVideotape25-0001 Purchase $245 Rental $25.

Women's Work: ManagementAnother in a series of documen-taries encouraging women toconsider careers in non-tradi-tional fields. Women in variousmanagement roles share theirexperiences, role conflicts,aspirations, and satisfactions.Minority women, in particular,discuss their unique status inthe management role.

29-min. 16 mm Color Eilm orVideotape25-0002 Rental $27 Purchase

*Write for purchase price.

RecursionVisiting Professor Joseph Stoyexplains and demonstrates theprocess of writing recursiveprograms, i.e. programs that'invoke themselves. Detailedexamples are illustrated (viz.three "monks" working on theTowers of Hanoi puzzle) and worked'out to clarify this frequentlymisunderstood topic.


41

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Demonstration of Sampling,Aliasing, and Frequency ResponseDemonstk'ation of sampling andaliasing with a sinusoidal signal.Sinusoidal response of a digitalfilter. Dependence of frequencyresponse on sampling period.Periodic nature of the frequencyresponse of a digital filter.


Measurement of Impulse ResponseDemonstration of the relativeinvariance of linear time-invariant system responses to thedetailed shape of a pulse inputof short duration but fixed area.


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SPECIAL PRCX;RAMS - Continued

Fourier Series DemonstrationApproximation representation ofa square wave by a sum of sineand cosine waves - even and oddfunctions, even and odd harmonics,Gibb's phenomenon, mean squareerror property.

15-min B&W Videotape13-0208 Purchase $115 Rental $20.

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4A Visit with J. Th. G. OverbeekThe serious lecturer of theColloid and Surface Chemistryseries gives way to the warmhuman being behind the theoriesand demonstrations. In an in-terview with John T. Fitch of theMIT Center for Advanced Engineer-ing Study, Theo Overbeek recountshis life story (beginning withhis "firm decision" not to be ateacher!) including the develop-ment of the D.L.V.O. theory.


Energy for the Year 2000A 1973 report by four MIT facultymembers interviewed by John Fitch.The factors contributing to theenergy crisis, a look at a com-puter model for predicting theeffects of off-shore drilling, avisit to a cryogenic generatorproject and a discussion ofenergy alternatives for the future.

29-min. Color Videotape25-00C3 Purchase $265 Rental $27.

The Management ofTechnological Innovation

Seven ColorVideotapes

For over a decade, theAlfred P. Sloan School ofManagement at MIT has carried outa broad research program on theeffective management of researchand development and on the com-mercial implementation oftechnological innovations. SixSloan School faculty membersreport the status of that re-search in a late 1975 symposiumfor members of the MIT IndustrialLiaison Program.

Motivating Scientists andEngineersProfessor Ralph Katz.One of the major issues in everyR&D setting. Recent research find-ings and contemporary views aboutmotivation. Differences from clas-sical perspectives and even fromviews popular in the '60s.

::40-min. Color Videotape25-0201 Purchase $200. Rental $50.

Uses Needs and IndustrialInnovationProfessor Eric Von Hippel.How to transfer an accurateunderstanding of user need to themanufacturer. User dominated,manufacturer dominated, andsupplier dominated modes.


Technical Venture StrategiesProfessor Edward B. Roberts.Entrepreneurial alternatives:Investments in small companies,joint ventures and new venturespinoffs, and internal venturegeneration. Directions forenhancing new venture results.


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Communication in Science and Preparations for ExperimentsTechnologyProfessor Thomas J. Allen. in ElectrophysiologyTechnical problem-solving orientedcommunication at the organizational, Dissection of a Frog, Part 1:inter-organizational, and national Sartorius Muscle - J.J. Guinan,Jr.levels. Keeping the organization Demonstrates how to pith a frogabreast of current technology and and how to remove a muscle in athe most effective techniques for way which will make the muscletransferring technology. suitable for intercellular

Z40-min. Color Videotaperecording.

25-0204 Purchase $200 Rental $50. 14-min. Color Videotape25-0301 Purchase $140 Rental $20.

Corporate /R&D Interface ManagementDr. William H. Gruber..How performance of corporate /R&Ddivisions is determined bymanagement policies and actionswhich affect the interfacebetween R&D and the rest of thecorporation. A strategy forimproving performance.


Innovation in IndustrialOrganizationsProfeasor_James Utterback, MITCenter for Policy Alternativesand Harvard Business School.The changing relationship betweenproduct and production processtechnologies as a central factor indetermining a firm's capabilitiesfor innovation to meet changingcompetitive conditions. Variableswhich can be manipulated bycorporate management, scientists,and engineers.


MANAGEMENT OF TECHNOLOGICALINNOVATION - Complete Set

Those renting or purchasing thecomplete set of six color video-tapes will receive - at no extra,cost - a 40-minute question andanswer session with all sixspeakers.

Seven Color Videotapes25-1200 Purchase $120030-Day Rental $300

Dissection of a Frog, Part 2:Gastrocnemius Muscle and itsInnervation J.J. Guinan, Jr.Demonstrates how to remove agastrocnemius muscle and itsinnervation, extending from themuscle to the spinal cord.


Dissection of a Frog, Part 3:Sciatic Nerve - J.J. Guinan, Jr.A method for dissecting out themain nerve trunk from the spinalcord to the ankle.


Electrophysiology of the FrogHeart - R.G. MarkDissection to expose beating heartof large pithed frog. Recordingof ECG with Ag-AgC1 electrodes.Use of suction electrodes torecord electrical activity ofvarious portions of heart. Cor-relation of these signals withobserved mechanical behavior andECG waveforms.


(Continued on inside back cover.)

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ORDERING INFORMATION

To order, use the postage-freeOrder Form on the next page ormail your Purchase Order to:

Center for Advanced EngineeringStudy. Room 9-232Massachusetts Institute ofTechnologyCambridge, Mass. 02139

Please provide all informationrequested on the Order Form, i.e.zip codes, format desired, catalognumbers, titles, prices, anddates required.

Note: Don't overlook the specialdiscounted prices for rentals andpurchases of complete sets.

Rentals

Rental period is five (5) daysper film or videotape. Forgreater scheduling flexibility,complete set rentals are recom-mended because of the longerrental period. Also note thediscounts available when rentingcomplete sets.

Purchases

Substantial discounts are offeredfor purchases of complete sets.Also note that rental fees can beapplied toward purchase price if Iorder is received within 30 daysafter rental period. Orders lessthan $20.00 must be pre-paid.

Previews

Preview period is three (3) days.Film or tape must be returnedimmediately thereaftr. Previewfilms and tapes are.!availableonly for prospective purchase.

Formats

All lectures and demonstrationslisted in this catalog areavailable as videocassettes andvideotapes. Many black-and-white (B&W) programs are alsoavailable as l6'.= films. Besure to check the appropriatebox in the order form to indicate -the format you want.

Delivery

Please reserve films and video-tapes at least two weeks beforescreening date to allow timefor shipment. On complete setrentals, you may wish to sug-gest a screening schedule.

All shipments will be made byU.S. Postal Service, pre-paidand insured, F.O.B. destination,unless otherwise instructed.Shipment by other carriers areF.O.B. Cambridge, Massachusetts.

Restrictions

All films, videotapes, and writtenmaterial in this catalog are copy-right by MIT and/or others. Allrights reserved. Reproductionof any part of these materials byany means is prohibited. The filmsand videotapes may not be used ontelevision or for paid fees oradmissions without the expresswritten consent of MIT.

Telephone: (617) 253-7444

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