sree saraswathi thyagaraja collegestc.ac.in/syllabus/2015-2016/m.sc_mathematics.pdf · z n4mma1t26...

Sree Saraswathi Thyagaraja College

(Autonomous)

(Affiliated to Bharathiar University and approved by UGC and certified by

9001: 2008 and accredited by NAAC with A Grade)

Palani Road, Thippampatti, Pollachi – 642 107

Knowledge Wisdom Compassion

Syllabus for PG Mathematics

2015-2016 Batch

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INDEX

Page No.

1 Scheme of Examinations & Syllabus

a. Scheme of Examinations 01-03

b. Semester-wise Syllabus 04-31

2 Autonomous Examination-Rules and Regulations

a. Examination Regulations 32-42

b. Grievance Form 43

4

1. Scheme of Examination and Syllabus

SREE SARASWATHI THYAGARAJA COLLEGE (Autonomous)

M. Sc (Mathematics)

Programme Structure

Batch Code: N4 Programme Code: MMA

With Effect from 2015-2016

SEM Spl COURSE

CODE Part S.No COURSE DETAILS

HRS/

WEEK CREDITS

MAX. MARKS

INT EXT TOTAL

I

Z N4MMA1T41 III 1 Core 1: Algebra 7 5 25 75 100

Z N4MMA1T42 III 2 Core 2: Real Analysis 7 5 25 75 100

Z N4MMA1T43 III 3 Core 3: Ordinary Differential

Equations 7 5 25 75 100

Z N4MMA1T04 III 4 Core 4: Java Programming and

Information security 5 4 25 75 100

Z N4MMA1P45 III 5 Core 5: Java Programming and

Information security –Lab 2 2 40 60 100

Z N4MMA1T26 Yoga for the Modern Age 3* 1# 50 - 50*

Library 2 - - - -

II

Z N4MMA2T31 III 6 Core 6: Measure and

Integration 5 5 25 75 100

Z N4MMA2T42 III 7 Core 7: Complex Analysis 6 5 25 75 100

Z N4MMA2T43 III 8 Core 8: Partial Differential

Equations 6 4 25 75 100

Z N4MMA2T44 III 9 Core 9: Quantitative Aptitude

& Verbal Reasoning 5 4 100 - 100

Z N4MMA2T45 III 10 Core 10: Latex 4 4 25 75 100

Z N4MMA2P46 III 11 Core 11: Latex - Lab 2 2 40 60 100

Z N4MMA2T27 Professional Ethics 3* 1# 50 - 50*

Library 2 - - - -

** Project carries 80 marks Internal (based on I, II and Final review) and 120 marks external (80% for evaluation

and 20% for viva voce)

SEM SPL COURSE

CODE Part S.No COURSE DETAILS

HRS/

WEEK CREDITS MAX. MARKS

INT EXT TOTAL

III

Z N4MMA3T41 III 12 Core 12: Topology 6 5 25 75 100

Z N4MMA3T22 III 13 Core 13: Functional

Analysis 5 4 25 75 100

Z N4MMA3T43 III 14 Core 14: Classical

Dynamics 6 5 25 75 100

Z N4MMA3T44 III 15 Elective I: Control Theory/

Mathematical Statistics 5 4 25 75 100

Z N4MMA3T45 III 16

Elective II: Number

Theory/

Magneto Hydrodynamics

6 5 25 75 100

Z N4MMA3T26 III 17 Communication for

Executives 5* 4# 25 75 100*

Library 2 - - - -

IV

Z N4MMA4T21 III 18 Core 15: Operator Theory 6 5 25 75 100

Z N4MMA4T12 III 19 Core 16: Fluid Dynamics 6 5 25 75 100

Z N4MMA4T43 III 20

Elective III: Graph Theory

/ Advanced Operations

Research

6 5 25 75 100

Z N4MMA4T44 III 21

Elective IV: Fuzzy Logic

and Fuzzy Sets / Actuarial

Mathematics

6 5 25 75 100

Z N4MMA4R45 III 22 Core 17: Project 4 2 80 120** 200

Library 2 - - - -

Total 90 + 6# 2200 +

200*

Number of courses Total Credits

Core Courses 17 70

Elective Courses 4 20

Extra Credit Course 3# 4#

Total 21 courses + 3# courses 90 + 4#

Note: *-Extra hours & Extra marks, # - Extra Credits, **-Project report – 48*2 = 96 and Viva Voce –12*2 = 24

EXPANSION FOR THE TITLES

S.NO Serial Number

SPL Z For Compulsory one and A To X for Alternatives (Shall be Indicated along with Code Connected by a Hyphen

Mark)

CODE Code Number for Each of the Course

SEM I To X For First Semester To Last Semester (Six For UG Programmes And Four / Six / Ten For PG

Programmes)

PART I To V For UG Programmes And Blank Space For PG Programmes

TYPE Nature of the course

COURSE Title of the Paper

HOURS Contact Allocated for Each Course

CREDITS Credit Weightage Allocated for Each Course and Total for Each Programme

INT Maximum Internal Marks Allocated for Each Course

EXT Maximum External Marks Allocated for Each Course

TOTAL Maximum Total Marks Allocated for Each Course

12

SEMESTER I

ALGEBRA

Credits: 5 Course Code: N4MMA1T41

Hours per week: 7 Total instructional Hours: 90

Course objective:

To teach the students about the general concepts in Abstract Algebra and to give a

foundation in various algebraic structures.

Skills set to be acquired:

After the completion of the course the student will be able to understand all the

abstract concepts of Algebra and will be able to solve the problems.

UNIT I (18 Hours)

Group Theory: Another counting principle - Sylows theorem. Ring Theory: Definitions and

Examples of rings – Special cases of rings – Homomorphisms

UNIT II (18 Hours)

Ring Theory: Ideals and Quotient rings – more ideals and quotient rings – The field of

quotients of an Integral domain

UNIT III (18 Hours)

Ring Theory: Euclidean rings – A particular Euclidean ring – Polynomial rings –

polynomials over the rational fields.

UNIT IV (18 Hours)

Fields: Extension field – roots of polynomials - more about roots.

UNIT V (18 Hours)

Fields: Elements of Galois Theory – Finite fields

Unit I : Chapter 2 - Section 2.11 - 2.14, Chapter 3, Section 3.1 – 3.3

Unit II : Chapter 3 - Sections3.4 - 3.6

Unit III: Chapter 3 - Section 3.7 – 3.10

Unit IV: Chapter 5 - Sections 5.1, 5.6, Chapter 7, Section 7 .1

Unit V : Chapter 5 - Sections 5.6 only.

TEXT BOOK:

I.N Herstein, Topics in Algebra, , John Wiley and Sons, Newyork, 2nd Edition 2003.

REFERENCE BOOKS:

1. P. B. Bhattacharya, S. K. Jain, S. R. Nagpaul, Basic Abstract Algebra,

Cambridge University Press, 2007.

2. J. B. Fraleigh, A First Course in Abstract Algebra, Narosa Publishing House,New Delhi,

VII Edition,2007.

3. Surjit singh, Linear Algebra, Vikas publications, 2011.

SEMESTER I

REAL ANALYSIS



Course Objective: To teach the functions about Metric Spaces, Continuous functions on

MetricSpaces, Connectedness, Completeness, Compactness and Riemann Integral and about

convergence of sequences and series of functions.

Skill sets to be acquired:

After the completion of Course the Student will be able to understand the concept of Open

sets,Closed Sets,Continuous functions on Metric Spaces, Uniform Continuity ,Riemann

Integrals, Laws of Derivatives,Pointwise Convergent and Convergence of Sequence of

Functions

13

UNIT I: (18 Hours)

Continuous functions on Metric Spaces: Functions Continuous at a point on the Real Line-

Reformation-Functions Continuous on the Metric Space-Open sets-Closed sets-

Discontinuous functions on R1-Simple Problems.

UNIT II: (18

Hours)

Connectedness, Completeness and Compactness: More about Open Sets-Connecetd sets-

Bounded sets and totally bounded sets-Complete Metric Spaces- Simple Problems.

UNIT III: (18 Hours)

Connectedness, Completeness and Compactness: Compact Metric Space- Continuous

functions on a Compact Metric Spaces-Continuity of the inverse function-Uniform

Continuity- Simple Problems.

UNIT IV: (18 Hours)

Calculus: Sets of Measure Zero-Definition of the Riemann Integral –Derivatives-Roll’s

Theorem-The law of the Mean-Fundamendal theorems of Calculus-Simple Problems.

UNIT V: (18 Hours)

Sequences and series of functions: Pointwise Convergence of the sequences of functions-

Uniform convergence of sequences of functons-Consequences of Uniform Convergence -

Convergence and Uniform Convergence of Series of functions-Integration and differention of

series of functions-Abel Summability.

TEXT BOOK:

1.Richard R.Goldberg, Methods of Real Analysis,Oxford & IBH publishing House, New Delhi,1970.

UNIT I : Chapter 5 - Sections 5.1-5.6.

UNIT II : Chapter 6 - Sections 6.1-6.4.

UNIT III : Chapter 6 - Sections 6.5-6.8

UNIT IV : Chapter 7 - Sections 7.1-7.8

UNIT V : Chapter 9 - Sections 9.1-9.6

REFERENCE BOOKS: 1. D.Somasundaram, B.Choudhary, A first Course inMathematical Analysis, Narosa

publishing House, 2010.

2. Charles Chapman Push, Real Mathematical Analysis, Springer International Edition, 4th Ed, 2013.

3. Russell A.Gordon, Real Analysis, Pearson Education Publication,2nd Ed,2002.

SEMESTER I

ORDINARY DIFFERENTIAL EQUATIONS



Course Objective: To learn Mathematical methods to solve higher order differential

equations and apply to dynamical problems of practical interest.

Skill sets tobe acquired: After the completion of the course the students will be exposed to

several methods of solvingordinary differential equations, boundary value problems and

stability theory.

UNIT I (18 Hours)

Linear differential equations of higher order: Wronskian – Variation of parameter.

Solutions in power series: Second order liner equations with ordinary points – Legendre

Equation & Legendre Polynomials – Second order equations with regular singular points –

properties of Bessel function.

14

UNIT II (18 Hours)

Systems of Linear differential equations: Systems of first order equations – Model for

Arms competition between two nations - existence and uniqueness theorem.

UNIT III (18 Hours)

Systems of Linear differential equations: Fundamental Matrix non-homogenous linear

system – linear systems with constant coefficients.

UNIT IV (18 Hours)

Existence & Uniqueness of solutions: Successive approximation – Picard’s theorem – Some

examples – continuation and dependence on initial conditions, Existence of solutions in the

Large – Existence and uniqueness of solutions of systems.

UNIT –V (18 Hours)

Boundary value problems: Introduction – strum- Liouvillie problem –Green’sfunction.

Oscillations of second order Equations: fundamental results –sturm’s comparison theorem.

TEXT BOOK:

S.G.Deo, V, Lakshmikantham, V.Ragavendra, Ordinary Differential Equations, Tata

McGraw –Hill Publishing Company ltd, (second edition), 2009.

Unit I : Chapter 2&3 - Section: 2.7, 2.8, 3.2, 3.3, 3.4 &3.5

Unit II : Chapter 4- Section: 4.2, 4.3 & 4.4

Unit III: Chapter 4- Section: 4.5, 4.6 & 4.7

Unit IV: Chapter 5- Section: 5.3, 5.4, 5.5, 5.6, 5.7, and 5.8

Unit V : Chapter 7&8 - Section: 7.1, 7.2, 7.3, 8.1, 8.2

REFERENCE BOOK:

1. Earl A. Coddington, An Introduction to Ordinary differential equations, PHI Learning

PVT, 2009.

2. B.Rai, D.P. Choudhury, Ordinary Differential Equations an introduction, Narosa

Publishing House, 2011.

3. D.Somasundram, Ordinary Differential Equations (A first course) NarosaPublishing

House. 2010

SEMESTER I

PROGRAMMING IN VISUAL BASIC



Course objective: To teach the student to solve mathematical, scientific, and business

problems using visual/ component based programming

Skill sets to be acquired: After the completion of the course the student will acquire

knowledge in applying visual programming to software creation by designing projects with

menus and submenus.

UNIT I (10 Hours)

The Visual Basic Environment: The initial Visual Basic screen – Toolbars – The Toolbox–

The initial form window – Project Explorer – Menu bar – Starting a new project – The

properties window – common form properties.

UNIT II (10 Hours)

Building the User Interface: Creating controls – The code window – Visual Basic’s Editing

Tools – Statements in Visual Basic –Variables – Data types – Working with variables –

constants – Determinate Loops –Indeterminate Loops – Making Decisions – Select Case –

Nested If – The Go To statement.

UNIT III (10 Hours)

String Functions – The Like Function – The Rnd Function – Numeric Function –

Date and Time Function – Function Procedures – Sub Procedures –Passing by Reference –

Passing by Value – Subprograms – Arrays.

15

UNIT IV (10 Hours)

Windows Common Controls: Common Dialog Boxes – Rich Text Box – Image list control

– Control – Tool Bar Control - Tree View Control. Menus: Menu Editor – Working with

Menus at Run Time

UNIT V (10 Hours)

Database Development: Using the Data Control – Methods and Events for the Data Control

– Monitoring changes to the Database – The Data Form Wizard – ActiveX Controls – Testing

the control – Adding the functionality.

TEXT BOOK:

Gary Cornell, Visual Basic 6 from the GROUND UP, Tata McGraw Hill Edition, 2013.

REFERENCE BOOKS:

1. D.S. Rajendra Prasad ,Visual Basic 6.0 – A simple Approach, Sapna Book House,

Bangalore

2. Visual Basic 6.0 Programming – Content Development Management, Chennai, 2010.

3. Ivan Bayross, Programming in Visual Basic, BPB Publications, 2006.

SEMESTER I

PROGRAMMING IN VISUAL BASIC - LAB



1. Write a program to calculate the simple and compound interest.

2. Using Timer Control set the time to display message.

3. Write a simple VB program to develop a calculator with basic operation.

4. Write a simple VB program to add the items to list box with user input and move the

selecteditem to combo box one by one.

5. Design a form using common dialog control to display the font, save and open dialog box

without using the action control property.

6. Write a simple VB program to accept a number as input and convert them into

a. Binary b. octal c. Hexa-decimal

7. Writing code for keyboard and mouse events

8. Database applications using data control for student mark list.

SEMESTER II

MEASURE AND INTEGRATION



Course Objective: To teach the students about the basic course in Lebegue measure, signed

measure and their derivatives.

Skill sets to be acquired: After the completion of the course the students will be able to

understand measure on the real line, integration of function of a real variable and Lp-spaces.

UNIT I (12 Hours)

Lebesgue measure: Introduction-Outer Measure- Measurable sets and Lebesgue Measure-

Measurable functions-Littlewoods’s three principles

UNIT II (12 Hours)

The Lebesgue Integral: The Lebesgue integral of a bounded function over a set finite

measure-The integral of a nonnegative function-The general lebesgue integral and

convergence in Measure.

UNIT III (12 Hours)

Differentiation and Integration: Differentiation of Monotone functions-Functions of bounded

variation-Differentiation of an integral-Absolute continuity.

16

UNIT IV (12 Hours)

Measure and integration: Measure spaces-Measurable functions-

Integration – General Convergence Theorems.

UNIT V (12 Hours)

The Radon-NikodymTheorem: Signed measures-The Raydon - Nikodym Theorem-The L p

Spaces.

TEXT BOOK:

H.L. Royden, Real Analysis, Macmillan Publishing company, U. S. A. Third Edition

Unit I : Chapter 3- section 3. 1, 3.2, 3.3, 3.5, 3.6

Unit II: Chapter 4-section 4.2, 4.3, 4.4, 4.5

Unit III:Chapter 5-section 5. 1, 5.2, 5.3, 5.4

Unit IV: Chapter 11- section11. 1, 11.2, 11.3, 11.4

Unit V: Chapter 11-section 11. 5,11. 6, 11.7

REFERENCE BOOK:

Measure theory and integration G.de Barra, First Edition, New age international Publishers.

SEMESTER II

COMPLEX ANALYSIS



Course Objective: To lay foundation for Topics in Advanced Complex Analysis.

Skill sets to be acquired: After the completion of the course the student will be able to

understand the applications of Conformal mapping and Contour integration which basics for

research activities in Applied Mathematics like Fluid Dynamics.

UNIT I (15 Hours)

Analytic functions: Cauchy Riemann Equations – Theorems and Problems – Analyticity:

Theorems and Problems – Harmonic Functions: Definition – Theorems and Problems.

Power Series: Maclaurin and Taylor’s Series – Operations on Power Series.

UNIT II (15 Hours)

Complex integration and Cauchy’s theorem – Curves – Parameterisation – Line integrals –

Cauchy’s theorem – Application of Cauchy’s theorem – Cauchy’s integral formula – Cauchy’s

inequalities and Applications – Maximum modulus theorem.

UNIT III (15 Hours)

Laurent’s Series and Residue theorem: Laurent’s series – Classification of singularities –

Evaluation of integrals – Argument principles – Rouche’s theorem – Hurwitz’s theorem –

Fundamental theorem of Algebra.

UNIT IV (15 Hours)

Harmonic functions: Comparision with Analytic functions – Theorems and problems – Mean

value property – Maximum principle for harmonic functions – Borel-Caratheodory theorem –

Positive harmonic functions: Harmack’s inequality – Harmack’s principle and theorems,

simple problems.

UNIT V (15 Hours)

Conformal mapping and the Riemann mapping theorem: Definition of Conformal mapping

and theorems – Normal families – Definition and theorems – Riemann mapping theorem:

Theorems and Examples.

17

TEXT BOOK

S. Ponnusamy and Herb Silverman, Complex Variables with Applications, Birhouser

Publishing, 2005.

Unit I: Chapter 5 - Sec: 5.1 – 5.3; Chapter 6 - Sec: 6.2 – 6.4

Unit II: Chapter 7 - Sec: 7.1 – 7.8; Chapter 8 - Sec: 8.1 – 8.3

Unit III: Chapter 9 - Sec: 9.1 – 9.4

Unit IV: Chapter 10 - Sec: 10.1 – 10.3

Unit V: Chapter 11 - Sec: 11.1 – 11.3

REFERENCE BOOKS

1. James Ward Brown, Ruel V. Churchill, Complex Variables and Applications, McGraw-Hill

Internation, 8th

Edition, 2009.

2. H.S.Kasana, Complex variables theory and applications PHI Publcations, 2nd

Edition, 2008.

SEMESTER II

PARTIAL DIFFERENTIAL EQUATIONS



Course Objective: To give an introduction to Mathematical techniques in analysis of Partial

Equations.

Skill sets to be acquired: After the completion of the course the student will be able to solve

Elliptic, Parabolic, Hyperbolic Partial Differential Equations.

UNIT I

First Order PDE: Solutions of linear first order PDE (Lagrange’s Method) – Integral

surfaces passing through a given curve – Surfaces orthogonal to a given system of surfaces –

compatibility of First Order PDE – Classification of solution of First Order PDE – Solution of

non-linear PDE of first order – Charpit’s method – Jacobi method- Special types of First

Order Equation – Cauchy’s method of Characteristics.

(SEC: 1.4 to 1.9)

UNIT II

Second Order PDE: Origin of II order PDE – Linear PDE with constant coefficients –

Methods solving linear PDE: Solutions of reducible equations - solutions of irreducible

equations with constant coefficients – rules for finding Complementary functions - rules for

finding Particular Integrals – Classification of II order PDE: Canonical forms.

(SEC: 2.1 to 2.4)

UNIT III Elliptic Differential Equations: Occurrence of Laplace and Poisson Equation – Boundary

value problems – Separation of variables method – Laplace in Cylindrical, Spherical

coordinates, Dirchlet & Newman problems for circle, sphere.

(SEC: 3.1 to 3.9)

UNIT IV Parabolic Differential Equation: Occurrence of the differential equation – Boundary conditions

- Separation of variables method – Diffusion equations in Cylindrical – Spherical coordinates.

(SEC: 4.1 to 4.5)

UNIT V Hyperbolic Differential Equations: Occurrence of wave equation – One dimensional wave

equation – Reduction to canonical form – D’Alembertz solution – Separation of variables

method – Periodic solution: Cylindrical, Spherical coordinates.

(SEC: 5.1 to 5.6)

18

TEXT BOOK:

1. J.N.Sharma and Kehar Singh, Partial Differential Equations for Engineers and Scientists,

Narosa Publishing House, Edition 2009.

REFERENCE BOOKS:

1.K.Sankara Rao, Introduction to Partial Differential Equations, PHI Publications, Edition

2009.

2. Lawrence C.Evans, Partial Differential Equations, American Mathematical Society, Edition

2009.

3.M.D. Raisinghania, Ordinary &Partial Differential Equations, S.Chand Publications, Edition

2011.

SEMESTER II

QUANTITATIVE APTITUDE AND VERBAL REASONING

(Common for MBA / MCA / MSW/ M.Com/ MIB/ M.Sc (CS) Students admitted from

2012 onwards)



Course Objectives: To inculcate the managerial and problem solving skills among the

students.


develop reasoning skills and face any competitive examinations with confidence.

UNIT I (12 Hours)

Averages : Page 139 to 3

Problem on Numbers : Page 161 to Page 167

Problems on Ages : Page 182 to Page 184

Simple Interest : Page 445 to Page 451

Compound Interest : Page 466 to Page 473

UNIT II (12 Hours)

Profit and loss : Page 251 to Page 260

Time and work : Page 341 to Page 346

Time and Distance : Page 369 to Page 384

Problems on trains : Page 405 to Page 409

Data interpretation : Page 661 to 669,683 to 688,695 to 704.

UNIT III (12 Hours)

Analogy : Page. 35 to Page 73

Coding and Decoding : Page 194 to 205 & Page 237 to 247

Blood Relations : Page 261 to Page 267

UNIT IV (12 Hours)

Direction sense Test : Page 416 to Page 421

Logical Venn diagram : Page 443 to Page 475

Number of ranking and Time Sequence test: Page 542 to Page 558

UNIT V (12 Hours)

Insert the missing character : Page 628 to Page 644

Data sufficiency : Page 654 to Page 662

Situation reaction Test : Page 731 to Page 747

Series completion : Page 1 to Page 15

TEXT BOOKS:

19

1. Dr. R.S.Agarwal, Quantitative Aptitude for Competitive Exams- S.Chand and Company,

2012 Edition, New Delhi (for units I & II only).

2. Dr.R.SAggarwal, A Modern Approach to Verbal and Non-Verbal Reasoning –, S.chand

and company, 2011 edition, New Delhi (For units III, IV, V).

REFERENCE BOOKS:

1. Abijit Guha, Quantitative Aptitude for Competitive Exams –Tata McGrawHill 3rd

Edition

2. B.S.Sijwali, Reasoning Verbal and Non Verbal, Arihant Publications 2007

LATEX

Hours per week: 4 Course Code : N4MMA2T25

Credits: 4 Total instructional Hours: 50

Objective : To teach the students about the applications of Latex.

Skill sets to be acquired : After the completion of the course the student will be able to

understand the basic concepts of Latex and will be able to program in Latex.

Unit I (10 Hours)

Introduction: Text formatting - Just what is LATEX? ; Markup Languages – Tex and its offspring’s - Basic

of a LATEX file.

Unit II (10 Hours)

Text, Symbols and Commands:

Commands names and arguments – Environments - Declarations – Lengths - Rubber lengths;

Special characters - Exercise – Fine-tuning text.

Unit III (10 Hours)

Document Layout and Organization: Document class – page style – Parts of the document – Table of contents; Displayed Text:

Changing font - Centering and indenting - Lists - Theorem-like declarations – Tabulator

stops.

Unit IV (10 Hours)

Boxes: LR boxes – parboxes and minipages – problem with vertical placement - paragraph boxes of

specific height – Rule boxes; Tables: Constructing tables – Table style parameter – Table

example.

Unit V (10 Hours)

Document preparation:

Letter writing – Question Paper settings - Article formation

Text Book:

H. Kopka and P.W. Daly, A Guide to LATEX , Addison – Wesley Longman Ltd, England,

fourth Edition, 2004.

Unit I : Chapter 1 : Sections : 1.1-1.3, 1.5.

Unit II : Chapter 2 : Sections : 2.1-2.7.

Unit III : Chapter 3 : Sections : 3.1-3.6, 4.1-4.3,4.5-4.6.

Unit IV : Chapter 4 : Sections : 4.7-4.8..

Reference Books:

1. Lamport L.(1985). LATEX – A Document preparation system. Reading MA:

Addision-Wesley.

2. Lamport L. (1994). LATEX – A Document preparation system. Reading. 2nd edn.

for LATEX2e. Reading MA: Addison-Wesley.

3. Schwarz N. (1990). Introduction to TEX. Reading MA: Addision-Wesley.

4. Snow W.(1992). TEX for the Beginner. Reading MA: Addision-Wesley.

20

LATEX - Lab

Hours per week: 2 Course Code : N4MMA2P26


1. Write a program to display Paragraph format

2. Write a program to display the definition

3. Write a program to display the trigonometry function

4. Write a program to display figure

5. Write a program to display theorem with proof

6. Write a program to display the mathematical problem with solution

7. Write a program to display the table content

8. Write a program to display the text content & body of the letter

9. Write a program to display the matrices

10. Write a program to display document

SEMESTER III

TOPOLOGY



Course Objective: To understand modern pure mathematics and to lay foundation for further

study in algebraic topology.

Skill sets to be acquired: After the completion of the course the student will be able to use

the methods in Topology to analyze Geometry.

UNIT I ( 12 Hours ) Topological Spaces and Continuous Functions: Topological Spaces-Basis for a Topology-

The Order Topology –The Product Topology on X x Y-The Subspace Topology- Closed Sets

and Limit Points.

UNIT II ( 12 Hours ) Topological Spaces and Continuous Functions: Continuous Functions-The Product Topology

–The Metric Topology-The Metric Topology (continued). The Quotient Topology (only

Theorem 22.1).

UNIT III ( 12 Hours ) Connectedness and Compactness: Connected Spaces – Connected Subspaces of the Real line

– Components and Local Connectedness- Compact Spaces – Compact Subspaces of the Real

line.

UNIT IV ( 12 Hours ) Connectedness and Compactness: Limit Point Compactness – Local Compactness.

Countability and Separation Axioms: The Countability Axioms – The Separation Axioms-

Normal spaces.

UNIT V ( 12 Hours ) Countability and Separation Axioms:The Urysohn Lemma – The Urysohn Metrization

Theorem-The Tietze Extension Theorem. The Tychonoff Theorem: The Tychonoff Theorem

– The Stone – Cech Compactification.

TEXT BOOK: James R Munkres, Topology, Second Edition, Prentice-Hall of India PVT Ltd. 2009.

Unit I: Chapter 2 - sections: 12, 13, 14, 15, 16, 17

Unit II: Chapter 2 - sections : 18, 19, 20, 21, 22

Unit III: Chapter 3 - sections: 23, 24, 25, 26, 27

Unit IV: Chapter 3 - sections: 28, 29, Chapter 4 - sections : 30, 31, 32

Unit V: Chapter 4 - sections: 33, 34, 35, Chapter 5 - sections : 37, 38

21

REFERENCE BOOKS: 1. H.Croom Fred, Principles of Topology, Cengage learning India Private ltd, Reprint 2009.

2. K.D.Joshi, Introduction to General Topology, Wiley Eastern Ltd., 2009.

SEMESTER III

FUNCTIONAL ANALYSIS



Course Objective: To teach the students about Banach spaces and about various operators.


understand the basic concepts of Banach spaces and to apply theorems on Banach spaces.

UNIT I (12 Hours) Normed Linear Spaces: Norm on a linear space-Examples of Normed linear spaces –

Seminorms and Quotient spaces-product space and Graph norm-Inner product spaces-Semi

inner product and sesqui-linear form(omit Ex 2.5).

UNIT II (12 Hours) Banach spaces: Banach spaces-Incomplete normed linear spaces(omit thm 2.28,Ex 2.8)

Completion of Normed linear spaces-Some properties of Banach spaces-Baire category

theorem(Statement only)-Heine Borel theorem and Riesz lemma-Best Approximation

theorems-Projection theorem.(omit Example 2.7(iii-vii) pg no 80-84)

UNIT III (12 Hours) Operators on Normed Linear spaces: Bounded operator (Omit Example 3.1(viii),3.2)Some

Basic results and Examples-The space B(x,y) - Norm on B(x,y) (omit Ex 3.3) and omit some

estimates for norms of certain properties – (pg no 137-150)-Riesz Representation Theorem-

Completeness of B(x,y)-Bessel’s Inequality-Fourier Expansion and Parsevals’s formula-

Riesz Fischer Theorem.

UNIT IV (12 Hours) Hahn Banach Theorem and Its Consequences: The Extension Theorem –Consequences –On

Uniqueness of Extension. Uniform Boundedness Principle: The Theorem and Its

Consequences.

UNIT V (12 Hours) Closed Graph Theorem and its Consequences: Closed Graph theorem-Bounded inverse

Theorem-Open Mapping theorem-A Stability Result for Operator Equations.

TEXT BOOK: M. Thamban Nair, Functional Analysis A First Course, Prentice-Hall of India. 2008

Unit-I: Chapter 1-sections 2.1, 2.1.1, 2.1.2, 2.1.4, 2.1.5, 2.1.6

Unit-II: Chapter 2-sections 2.2, 2.2.1, 2.2.2, 2.2.3, 2.4, 2.5, 2.6

Unit-III: Chapter 3-sections 3.1, 3.1.1, 3.2, 3.2.1, 3.3, 3.4.1 ; Chapter 4-sections 4.2, 4.3, 4.4

Unit-IV: Chapter 5-sections 5.1, 5.2, 5.3 ; Chapter 6- section 6.1

Unit-V: Chapter 7-sections 7.1, 7.2, 7.3, 7.3.1

REFERENCE BOOKS:

1. Balmohan V. Limaye ,Functional Analysis, 2nd

Edition,2003.

2. G.F Simmons, Introduction to Topology and Modern Analysis, McGraw Hill,

International Book company, International student Edition 1963.

22

SEMESTER III

DIFFERENTIAL GEOMETRY



Course Objective: To teach the students a few applications of Abstract Algebra and analysis

to geometrical problems and facts.


understand elementary theory of surfaces, fundamental theorem of surface theory.

UNIT I

Theory of Space Curves: Theory of space curves – Representation of space curves – Unique

parametric representation of a space curve – Arc-length – Tangent and osculating plane –

Principle normal and binormal – Curvature and torsion –Contact between curves and surfaces.

UNIT II

Theory of Space Curves (Contd.): Osculating circle and osculating sphere – Locus of centre of

spherical curvature – Tangent surfaces – Involutes and Evolutes –Spherical indicatrix-

Intrinsic equations of space curves – Fundamental Existence Theorem – Helices*.

UNIT III

Local Intrinsic properties of surface: Definition of a surface – Nature of points on a surface –

Representation of a surface – Curves on surfaces –Metric on a surface –The first fundamental

form– Families of curves – Orthogonal trajectories – Intrinsic properties

UNIT IV

The Second Fundamental form and local non-intrinsic properties of a surface:

The Second fundamental form-classification of points on a surface- principal curvatures-

Lines of curvature.

UNIT V

Geodesic on a surface: Normal property of Geodesics –Gaussian curvature

The Fundamental Equations of Surface Theory: Tensor Notations –Gauss equations –

Weingarten equations-Mainardi-Codazzi equations.

TEXT BOOK: D. Somasundaram, Differential Geometry, Narosa Publ. House, Chennai, 2005

Unit I: Chapter 1 - Sections 1.1 to 1.7, 1.10

Unit II: Chapter 1 - Sections 1.10 to 1.13 and 1.16 to 1.18 *: theorems only

Unit III: Chapter 2 - Sections 2.1 to 2..5, 2.9, 2.11, 2.12, 2.15

Unit IV:

Unit V: Chapter 3 - Sections 3.5 , 3.12 and Sections 5.1 to 5.5

REFERENCE BOOKS:

1. T. Willmore, An Introduction to Differential Geometry, Clarendan Press, Oxford, 1959.

2. D.T Struik, Lectures on Classical Differential Geometry, Addison – Wesely, Mass. 1950.

3. J.A. Thorpe, Elementary Topics in Differential Geometry, Springer – Verlag, New York,

1979.

SEMESTER III

JAVA PROGRAMMING

Hours per week: 4 Course Code: N4MMA3T45


Course Objective : To teach the students about the characteristics of the linear system.The

course covers al aspects of Cyber Security including network security, computer security and

information security.


understand observability, controllability, stability, stabilizability of the linear system.

23

UNIT I (10 Hours) Java History, Java Features, How Java Differs from C and C++, Java Environment, Java

Program Structure, Java tokens, Java Statements, Implementing a Java Program, Java Virtual

Machine, Command line Arguments, Constants, Variables, Data Types, Operators and

Expressions, Decision Making and Branching, Decision Making and Looping.

UNIT II (10 Hours)

Classes, Defining a Class, Adding Variables. Adding Methods, Creating Objects, Accessing

class Members, Constructors, Method Overloading, Static Members, Nesting of Methods,

Inheritance, Overloading Methods.

UNIT III (10 Hours)

Visibility Control Arrays, One Dimensional arrays, creating an Array, Two Dimensional

Arrays, Strings, Vectors, Wrapper classes, Interface: Multiple Inheritance.

Packages, Java API Packages, Using System Packages, Naming Conventions, Creating

Packages, Accessing a Package, Using a Package, Adding a class to Package.

UNIT IV (10 Hours)

Multithreaded Programming, Creating Threads, Extending the Thread Class, Stopping and

Blocking a Thread, Life Cycle of a Thread, Using Thread Methods, Thread Exceptions,

Thread Priority, Synchronization, Managing Errors and Exceptions

UNIT V (10 Hours)

Applet Programming, How Applet Differs from Applications, Preparing to write Applets,

Building an Applet code, Applet Life Cycle, Creating an Excutable Applet.

TEXT BOOK: 1.E. Balaguruswamy, Programming with Java, Tata McGraw Hill, IV Edition 2010.

REFERENCE BOOK: 1.PatricNaughton, Java Hand Book, Tata McGrawHill ,2008.

SEMESTER III

JAVA PROGRAMMING LAB


Credits: 2 Total instructional Hours: 40 1. Program to count the number of digits, alphabets and special characters in a string.

2. Program to read a string and rewrite it in Alphabetic order

3. Program to sort given n names

4. Program for Matrix Multiplication

5. Program to find the transpose of a square matrix, the sum of elements and largest

element

6. Program to sort the array of given names

7. Write a Java Program to implement the concept of multiple inheritance using

Interfaces.

8. Write a Java Program to implement the concept of multithreading with the use of any

three

Multiplication tables and assign three different priorities to them.

9. Designing a web page of our college having maximum of the WebPages.

10. Write a Java Program to draw line, circle, and ellipse using Applets.

24

SEMESTER IV

OPERATOR THEORY



Course Objective: To teach students about the linear operators.

Skill sets to be acquired: After the completion of the course the Students will be able to

understand the concepts of various operators and various inequalites.

UNIT I (15 Hours)

Compact operators: Some characterizations – Space of compact operators- Further

properties.

Spectral results for Banach space operators: Eigen spectrum and approximate Eigen

spectrum.

UNIT II (15 Hours)

Spectral results for Banach space operators: Spectrum and resolvent set – Integration of

Operator valued functions – Riesz – Schauder Theory

UNIT III (15 Hours)

Operators on Hilbert Spaces: Adjoint of an operator- Self adjoint, normal and unitary

operators –Hilbert –Schmidt Operator

UNIT IV (15 Hours)

Spectral results for Hilbert space operators: Some properties of the spectrum – More results

on th spectra of self adjoint operators.

UNIT V (15 Hours)

Spectral representations: Spectral representation of Compact self adjoint operators - singular

value representation of compact operators- Spectral representation of self adjoint operators.

TEXT BOOK:

M.Thamban Nair, Functional Analysis A First Course, PHI Learning Pvt, New Delhi 2010.

REFERENCE BOOK:

Balmohan Vilmage, Functional Analysis, New age international, 2010.

LIST OF ELECTIVES

FLUID DYNAMICS

Course Objective: To teach the students about the mathematical theory of fluid motion

which finds a larger applications in hydrodynamics and Aerodynamics.


understand general properties of fluid motion like velocity, acceleration of a fluid particle,

dynamical equation Vortices and will be able to solve two dimensional Laminar flow.

Preliminaries: Introduction – General Description – Isotropic – Some basic properties of

fluid – Viscous & Non – Viscous fluids – Viscosity – Newtonian & Non – Newtonian fluids

– Real & Ideal fluids – Some important types of flows .

Orthogonal curvilinear coordinates: Expression - Φ, ∇ × 𝑓 , ∇ . 𝑓 , ∇2 Φ in Orthogonal

curvilinear coordinates, Spherical, Cylindrical coordinates (Results only).

UNIT I

Kinematics of Fluid Motion : Methods of describing fluid motion- Lagrangian method -

Describing fluid method & problems - Velocity of a fluid particle –-Material, local

&convective derivatives - Acceleration of a fluid particle - Expression in different co-

ordinates - Simple problems- Significance of equation of continuity - Equation of continuity

by Euler method -Equation of continuity in Cartesian, Cylindrical, Spherical, Polar co-

25

ordinates, Equation of continuity by lagrangian methods - Illustrative solved examples -

Boundary conditions (Kinematical) & problems- Strem line, Streak line, Path line, Stream

tube& Stream filament & problems.

UNIT II

Vorticity vector- Vortex line - Vortex tube - Vortex filament - Rotational & Irrotational

motion- Angular velocity vector - Euler’s equations of motion of an inviscid fluid - Lamb’s

hydrodynamical equation- Conservative fluid of force – Euler’s equation of motion in

cylindrical & spherical coordinates and simple problems.

UNIT III

Motion in 2 Dimensions: Motion in 2 dimensions- Stream functions – Physical significance

of stream function – Irrotational motion in 2 dimension – Complex potential- C –R equation

in polar form – magnitude of velocity - Complex potential for some uniform flows – Simple

problems.

Sources and Sinks: Sources and Sinks in 2 Dimensions - Complex potential due to doublet

in 2 dimension -Simple problems

UNIT IV

Vortex Motion: Introduction- Vorticity- Vorticity component - Vorticity line, Vorticity tube,

Vorticity filament Helmholt’z Vorticity Theorem (properties of Vorticity tube) probl;ems-

Rectilinear vortices- Derivation of velocity potential- Velocity components and complex

potential due to a rectilinear vortex filament- Vorten pair - Vortex doublet.

UNIT V

The Navier- Stokes equation & the Energy Equation: The Navier- Stokes equation of viscous

fluid – Diffusion of vorticity - Vorticity transport equation . Some useful dimensional

numbers : Definitions and solved examples. Laminar flow of viscous incompressible

fluids:Limitations of t he Navier- Stokes equation – exact solution of the Navier- Stokes

equation – plane couette flow –Generalised couette flow- plane poiseullie flow- Hagien

poiseullie flow.

TEXT BOOK:

Dr.M.D.Raisinghania, Fluid Dynamics, S.Chand & company Ltd,2010.

REFERENCE BOOKS:

1. G.K.Batchelor, A introduction to Fluid Dynamics, Cambridge university press,2012

2. John F. Douglas, Janusz M. Gasiorek and John A.Swaffield, fluid Mechanics, Pearson .

Education Ltd. Fourth Edition, 2009.

NUMBER THEORY

Course Objective: To teach the students about the congruences , Quadratic reciprocity and

Arithematic function.

Skill sets to be acquired : After the completion of the course the student will be able to

know the significance of the Number Theory, the great attraction of the mathematicians in the

recent years and will be able to develop his problem solving skills.

UNIT I

Introduction, Divisibility, Primes.

UNIT II Congruences, solutions of congruences, Congruences of Degree 1. The functions (n),

congruences of higher degree, Prime power moduli, Prime modulus.

UNIT III Congruences degree 2, prime modulus, power Residues, Number theory from an algebraic

view point , Multiplicative groups, Rings and fields, quadratic residues.

26

UNIT IV

Quadratic reciprocity – The Jacobi Symbol – Greatest integer function.

UNIT V

Arithmetic functions – The Moebius Inversion formula – The multiplication of arithmetic

functions – Recurrence functions.

TEXT BOOK:

Ivan Nivan and Herberts Zucherman , An Introduction to Theory of Numbers, John Wiley&

Sons Inc, 5th

Edition, 2000.

Unit I: Chapter 1- Sections 1.1 – 1.3

Unit II : Chapter 2 - Sections: 2.1 – 2.7

Unit III: Chapter 2 - Sections: 2.8 – 2.11 ; Chapter 3 - Section: 3.1

Unit IV: Chapter 3 - Sections: 3.2, 3.3 ; Chapter 4 - Section: 4.1

Unit V: Chapter 4 - Sections: 4.2 – 4.5

REFERENCE BOOKS: 1. T.M. Apostol, Introduction to Analytic Number Theory, Springer Verlag, 8

th reprint, 1998.

2. Kennath and Rosan, Elementary Number Theory and its Applications, Addison Wesley

Pulishing Company, 1984.

3. George E. Andrews, Number Theory, Hindustan Publishing, New Delhi, 1989.

4. Kumaravelu & Susila kumaravelu, Elements of Number Theory, Raja Sankar off set

printers, 2002.

GRAPH THEORY

Course Objective: To teach the students about the basic and advanced concepts of Graph

Theory

Skill Sets to be acquired: After the complection of the course the student will be able to

understand matching, Degree Sequences and Colourability of the graphs which finds a lot of

applications in research.

UNIT I

Graphs and Subgraphs: Introduction – Definition and Examples –Degrees – Sub graphs –

Isomorphism – Ramsay Numbers – Independent Sets and Coverings – Intersection Graphs

and Line Graphs – Matrices – Operations on Graphs.

UNIT II

Degree Sequences: Introduction – Degree Sequences – Graphic Sequences; Connectedness:

Introduction – Walks, Trails and Paths – Connectedness and Components – Blocks –

Connectivity.

UNIT III

Eulerian and Hamiltonian Graphs: Introduction – Eulerian Graphs – Hamiltonian Graphs;

Trees: Introduction – Characterisation of Trees – Centre of a Tree.

UNIT IV

Matchings: Introduction – Matchings – Matchings in Bipartite Graphs; Planarity:

Introduction – Definition and Properties – Characterization of planar Graphs – Thickness,

Crossing and Outer Planarity.

UNIT V

Colourability: Introduction – Chromatic Number and Chromatic Index – The Five Colour

Theorem - Four Colour Problem – Chromatic Polynomials; Directed Graphs: Introduction -

Definition and Basic Properties – Paths and Connections – Digraphs and Matrices –

Tournaments.

27

TEXT BOOK:

S. Arumugam and S. Ramachandran , Invitation to Graph Theory, Scitech Publications

(India) Pvt. Ltd, 2006.

REFERENCE BOOKS:

1. S. Kumaravelu & Susheela Kumaravelu, Graph Theory, Janaki Calender Corporation,

Sivakasi, 1999

2. R. Balasubramanian and K. Ranganathan, Text Book on Graph Theory, Springer Verlog,

New York, 2000.

3. F. Harray, Graph Theory, Addison Wesley Company, 2001.

CONTROL THEORY

Course Objective : To teach the students about the characteristics of the linear system.


understand observability, controllability, stability, stabilizability of the linear system.

UNIT I

Observability : Linear Systems – Observability Grammian – Constant coefficient systems –

Reconstruction kernel – Nonlinear Systems

UNIT II

Controllability: Linear systems – Controllability Grammian – Adjoint systems – Constant

coefficient systems – steering function – Nonlinear systems

UNIT III

Stability: Stability – Uniform Stability – Asymptotic Stability of Linear Systems - Linear

time varying systems – Perturbed linear systems – Nonlinear systems

UNIT IV

Stabilizability: Stabilization via linear feedback control – Bass method – Controllable

subspace – Stabilization with restricted feedback

UNIT V

Optimal Control: Linear time varying systems with quadratic performance criteria – Matrix

Riccatiequation – Linear time invariant systems – Nonlinear Systems

TEXT BOOK: K.Balachandran and J.P.Dauer, Elements of Control Theory, Narosa, New Delhi, 1999.

Unit I: Sec 2.1, 2.2

Unit II: Sec 3.1, 3.2

Unit III: Sec 4.1, 4.2, 4.3

Unit IV: Sec 5.1, 5.2, 5.3

Unit V: Sec 6.1, 6.2, 6.3

MATHEMATICAL STATISTICS

Course Objective: To teach the students about the advance level of Statistics.


apply the statistical tools in real life situations.

UNIT I

Characteristic Functions: Properties of Characteristic functions – Necessary and sufficient

condition for (t) to be characteristic function – Inversion Theorem (Levy Theorem) –

Uniqueness theorem of characteristic function – Continuity theorem for characteristic

function – Chebychev’s Inequality

28

UNIT II

Some Probability Distributions: Negative Binomial Distribution – MGF of Negative

Binomial Distribution – cumulants of Negative Binomial Distribution – PGF of Negative

Binomial Distribution – Deduction of moments of Negative Binomial Distribution from

those of binomial Distribution – Rectangular Distribution – Weibul Distribution

UNIT III

Central Limit Theorems:The DeMoivre Theorem - The Lindeberg – Levy Theorem-

Application of central limit theorem – Liapounoff’s central limit theorem – Cramer’s

theorem.

UNIT IV

Exact Sampling Distribution - derivation of chi-square distribution – MGF of chi-square

distribution – Students t distribution – derivation of Students t distribution – Constants of

Students t distribution - limiting theorem of Students t distribution – F distribution –

derivation of F distribution – Constants of F distribution – Mode and points of inflexion of F

distribution.

UNIT V

Random process: Random process concepts – classification of random processes –

continuous random processes – Discrete random process - continuous random sequence –

Discrete random sequence – Non deterministic process – deterministic process - Stationarity

and independence – distribution and density function – First order stationary process –

strongly stationary process – jointly stationary in the strict sense – wide sense stationary –

evolutionary process – auto correlation of a random process – problems.

TEXT BOOK: 1. S. C. Gupta and V. K. Kapoor, Fundamentals of Mathematical Statistics, Sultan Chand &

Sons, Edition 2008.

2 A. Singaravelu & S. Sivasubramanian, Probability abd Random Process, Meenakshi

Agency, Edition 2008(Unit V Chapter 4: Page No. 4.1 to 4.36)

REFERENCE BOOKS: 1. R.S.N.Pillai And V.Bagavathi, Statistics , S.Chand & CO, 2010.

2. P.R.Vittal, V.Malini, Mathematical Statistics, Margham Publications, 2003.

3. W. Feller, An introduction to Probability Theory and Applications, New york.

FUZZY LOGIC AND FUZZY SETS

Course Objective: To teach the students about the notion of Fuzzy sets, Fuzzy relations and

measures of Fuzziness.


understand the applications of Fuzzy sets in Engineering, Social Sciences and Computer

Science.

Unit I

Crisp Sets And Fuzzy Sets: Introduction-Crisp sets: An over view-The Notion of Fuzzy Sets-

basic concepts of Fuzzy sets – Classical Logic: complement-Fuzzy Union-Fuzzy interaction –

Combination of operations – general aggregation of operations.

Unit II

Fuzzy Relations: Crisp and Fuzzy relations – Binary relations – Binary relations on a single

set –Equivalence and similarity relations – Compatibility on Tolerance Relations-Orderings –

Morphism – Fuzzy relations Equations.

29

Unit III

Fuzzy Measures:General discussion – Belief and plausibility Measures –Probability measures

– Possibility and Necessity measures – Relationship among Classes of Fuzzy Measures.

Unit IV

Uncertainty And Information:Types of Uncertainty – Measures of Fuzziness-Classical

Measures of Uncertainty –Measures of Dissonance-Measures of Confusion – Measures of

Non-Specificity – Uncertainty and Information – Information and Complexity – Principles of

Uncertainty and information.

Unit V

Applications:Natural, life and Social Sciences - Engineering - Medicine - Management and

decision making – Computer Sciences-System Science-Other Applications.

TEXT BOOK: George J. Klir and Tina A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-

Hall of India Private Limited, 2008 (Chapters 1 to 6)

REFERENCE BOOKS:

1.John Yuan, Reza Langari, Fuzzy Logic Intellegence, Control and Information, Pearson

Education, New Delhi, 1999.

2.M. Amirthavalli, Fuzzy logic and Neural Networks, Scitech Publications Pvt. Ltd, Chennai

and Hyderabad, 2007.

3. Timothy J. Ross, Fuzzy Logic with Engineering Applications, Mc Graw-Hill INC, New

York, 1996.

MAGNETOHYDRO DYNAMICS

Course Objective: To teach students the types of flow of a fluid in the presence of a

magnetic field.

Skill sets to be acquired: After the completion of the course the Students will be able to

understand, Alfven’s Theorem and its application, flow of fluids between parallel plates in

the presence of transverse magnetic field and gravitational stability.

UNIT I Electromagnetism – Fundamental Laws – Electrostatic Energy – Electrodynamics –

Ampere’s Law – Lorentz force on a moving charge – Magnetostatic Energy – Faraday’s Law

of Induction – Poynting stresses – Electromagnetic Equations with respect to moving axes –

boundary conditions of electric and magnetic fields.

UNIT II

Kinematics of fluid motion – equation of continuity – Stress tensor – Navier-stokes

equations – boundary condition – Velocity Magneto fluid dynamic equations – MHD

approximation – equation of Magnetic diffusion in a moving conducting medium – Magnetic

Reynolds number.

UNIT III

Alfven’s theorem Law of isorotation - Magneto hydrostatics – Force-free field – Alfven

waves in incompressible MHD.

UNIT IV

Incompressible viscous flows in the presence of magnetic field – Hartmann Flow –

unsteady Hartmann flow – Magnetofluid dynamic pipe flow.

UNIT V

Stability – Instability of linear pinch – Sausage and flute types – Method of small

oscillations – gravitational instability.

TEXT BOOKS:

1. Crammer K.R. and Pai S.I, Magneto Fluid Dynamics for Engineers and Applied

Physicists, McGraw Hill, 1973.

30

2. Ferraro, VCA and Plumpton: Introduction to Magneto Fluid Dynamics, Oxford, 1966.

ADVANCED OPERATIONS RESEARCH

Course Objectives: To throw light on the Industrial applications of Operations Research.

Skill sets to be acquired: After the completion of the course the students will be able to

solve problems on Dynamic Programming, Simulation, Non-Linear Programming.

UNIT I

Dynamic Programming : Introduction – The Recursive Equation Approach - Characteristics

of Dynamic Programming - Dynamic Programming Algorithm – Solution of Discrete D.P.P.

- Some Applications – Solution of L.P.P. by Dynamic Programming.

UNIT II

Simulation : Introduction – Why Simulation? – Process of Simulation - Simulation Models –

Event-Type Simulation – Generation of Random Numbers – Monte-Carlo Simulation –

Simulation of Inventory Problems – Simulation of a Queueing System.

UNIT III

Investment Analysis and Break-Even Analysis : Introduction – Time Value of Money –

Annuities and Sinking Fund – Methods of Investment Analysis – Investment under

Uncertainty(Risky Investments) – Decision Trees and Investment Analysis – Simulation

Approach to Risky Investment – Break-even Analysis.

Unit IV

Non-Linear Programming-Methods : Introduction – Graphical Solution – Kuhn-Tucker

Conditions with Non-Negative Constraints – Quadratic Programming – Wolfe’s Modified

Simples Method – Beale’s Method – Separable Convex Programming.

UNIT V

Information Theory : Introduction – A Measure of information – Entropy-The Expected

Information – Entropy as a Measure of Uncertainty – Some Properties of Entropy Function –

The Communication System – Channel Probabilities – Joint and Conditional Entropies –

Mutual Information – Encoding.

TEXT BOOK:

Kanti Swarup, P.K. Gupta, Man Mohan ‘Operations Research’ Sultan Chand & Sons, 2008

REFERENCE BOOKS:

1. J. K. Sharma, Operations Research Theory and Applications, Macmillan India Ltd., Third

Edition.

2. Billy E. Gillett, Introduction to Operations Research, A Computer Oriented Algorithm

Approach, Tata McGraw Hill Publishing Company Ltd.

3. Hamdy A. Taha, Operations Research An Introduction, Eighth Edition, Published by

Dorling Kindersley (India) Pvt. Ltd., licensees of Person Education in South Asia.

CLASSICAL DYNAMICS

Course Objective: To provide the students with the thorough knowledge in the fundamentals

of Classical Dynamics.

Skill sets to be acquired: After the completion of the course the student will be acquired

knowledge in solving Dynamical problems and to understand the motion of objects like

Planets, Rockets and Tops.

UNIT I

Lagrange Equation : Introduction – classification of a dynamical system – Lagrange’s

equations for simple systems – principles of virtual work – D’Alembert’s Principle -

Lagrange’s equations for general systems

31

UNIT II

Hamilton Equations : Hamilton Equations – ignorable coordinates – the Routhian function

UNIT III

Hamilton methods: Introduction – Hamilton’s principle

UNIT IV Characteristic function and Hamilton – Jacobi equation – phase space and Lioville’s theorem

UNIT V Special transformations – calculus of variations

TEXT BOOK: K. Sankara Rao, Classical Mechanics, PHI Learning Private Limited, New Delhi, 2009.

Unit-1: Chapter 6 - Section: 6.1 to 6.5

Unit-2: Chapter 6 - Section: 6.6 to 6.8

Unit-3: Chapter 7 - Section: 7.1, 7.2



REFERENCE BOOKS: 1. Herbert Goldstein, Classical Mechanics, Pearson Education, 2009.

2. Gupta, Kumar and Sharma, Classical Mechanics, A Publication of Pragati Prakashan,

India, 2003.

32

EXAMINATION SYSTEM UNDER AUTONOMY

1.Pattern of Examinations: The college follows semester pattern. Each academic year consists of two semesters and each semester ends with the End Semester Examination. A student should have a minimum of 75% attendance out of 90 working days to become eligible to sit for the examinations. 2.Internal Examinations: The questions for every examination shall have equal representation from the units of syllabus covered. The question paper pattern and coverage of syllabus for each of the internal (CIA) tests for PG programs other than MBA and MCA are as follows.

i) First Internal Assessment Test Syllabus : First Two Units Working Days : On completion of 30 working days, approximately Duration : Two Hours Max. Marks : 50

For the First internal assessment test, the question paper pattern shall be as given below.

Question Paper Pattern

Section A

Attempt all questions (three each from both units) 06 questions – each carrying one mark 06 X 01 = 06 No Choice

Section B Attempt all questions (two each from both units) 04 questions – each carrying five marks 04 X 05 = 20 Inbuilt Choice [Either / Or]

Section C Attempt all questions (Minimum one question shall be asked from each unit) 03 questions - each carrying eight marks 03 X 08 = 24 Inbuilt Choice [Either / Or] Reduce these marks to a maximum of 05 i.e., (Marks obtained/50) X 5 === A

ii) Second Internal Assessment Test

Syllabus : Third and Fourth Units Working Days : On completion of 65 working days approximately, Duration : Two Hours Max. Marks : 50

33

For the Second internal assessment test, the question paper pattern shall be as given below.


Section A

Attempt all questions 06 questions – each carrying one mark 06 X 01 = 06 No Choice

Section B

Attempt all questions (two each from both units) 04 questions – each carrying five marks 04 X 05 = 20 Inbuilt Choice [Either / Or]

Section C

Attempt all questions (Minimum one question shall be asked from each unit) 03 questions - each carrying eight marks 03 X 08 = 24 Inbuilt Choice [Either / Or] Reduce these marks to a maximum of 05 i.e., (Marks obtained/50) X 5 === B

iii) Model Examinations

Syllabus : All Five Units Working Days : On completion of 85 working days approximately, Examination : Commences any day from 86th working day to 90th working day. Duration : Three Hours Max. Marks : 75

For the model examinations, the question paper pattern shall be the same for all UG and PG programs, as given below.


Section A

Attempt all questions 10 questions – each carrying one mark 10 X 01 = 10 No Choice

Section B

Attempt all questions 05 questions – each carrying five marks 05 X 05 = 25 Inbuilt Choice [Either / Or]

34

Section C

Attempt all questions 05 questions – each carrying eight marks 05 X 08 = 40 Inbuilt Choice [Either / Or] Reduce these marks to a maximum of 10 i.e., (Marks obtained / 75) X 10 C The following is the Question Paper Pattern for the courses „Yoga for the Modern Age‟ & „Professional Ethics‟ Syllabus : All Five Units

Duration : Three Hours

Max. Marks : 50


Section A (5 x 10 = 50 marks)

Five Questions of “either / or” type. Each question carries 10 marks. Answer all questions Q.1 (a) ___________________ or

(b) ___________________

Q.2 (a) ___________________ or (b) ___________________

Q.3 (a) ___________________ or (b) ___________________

Q.4 (a) ___________________ or (b) ___________________

Q.5 (a) ___________________ or (b) ___________________

iv) Assignments

Each student is expected to submit at least two assignments per course. The assignment topics will be allocated by the course teacher. The students are expected to submit the first assignment before the commencement of first Internal Assessment Test and the second assignment before the commencement of second Internal Assessment Test. Typed/computer print outs and photo copies will not be accepted for submission.

Scoring pattern for Assignments

Punctual Submission : 2 Marks Contents : 4 Marks

35

Originality/Presentation skill : 4 Marks Maximum : 10 Marks x 2 Assignments = 20 marks

Reduce these marks to a maximum of 5 i.e., (Marks obtained / 20) X 5 === D

v) Seminars

Each PG student is expected to present the two assignments as seminar in the class.

Scoring pattern for Seminars

Logical and clear presentation : 3 Illustration : 3 Originality / Presentation skill : 4 Maximum : 10Marks x 2seminars = 20marks

Reduce these marks to a maximum of 5 i.e., (Marks obtained / 20) X 5 === F

Calculation of Internal Marks for all PG and Parallel programs:

1. Internal Assessment Test : Average of the two tests. Reduced to a Maximum of 05Marks (A+B)/2 2. Model Examination : Reduced to a Maximum of 10 Marks (C) 3. Assignment : Reduced to a Maximum of 05 Marks (D)

4. Seminars : Reduced to a Maximum of 05 Marks (F)

Internal Marks Scored = ((A + B)/2) + C + D + F

Calculation of Internal Marks for Yoga for the Modern Age & Professional

Ethics all PG

1. I Cycle Test : 50 marks test is reduced to the Maximum to 15

Marks

2. II Cycle Test : 50 marks test is reduced to the Maximum to 15

Marks 3. Model : 75 marks test is reduced to the

Maximum to 20

Marks -------------------

50Marks -------------------

36

vi) Practical Examination The Internal Assessment marks for practical examinations are based on

the following criteria. The assessment is for 40 % marks of each practical course.

I Cycle Test - 5 II Cycle Test - 5 Model - 10 Lab Performance - 12

Record - 8 -------- Total 40 --------

vii) Project and Viva Voce

The Project assessment will be done for 100 marks for each Project /

Research work. 40 marks for Internal assessment mark and 60 marks for External

assessment mark.

The Internal Assessment mark for project evaluation is based on the

following criteria.

a. I Review 20

b. Pre Final Review 30

c. Final Review 30

----------------- Total 80

--------------------

3. External Examinations:

The external examinations for theory courses will be conducted for 75

% marks, for all UG and PG degree programs. The external theory

examinations will be conducted only after the completion of 90 working days

in each semester.

Normally, the external practical examinations will be conducted before

the commencement of theory examinations. Under exceptional conditions

these examinations may be conducted after theory examinations are over.

The external evaluation will be for 60 % marks of each practical course.

The External Assessment marks for practical examinations are based on

the following criteria. The assessment is for 60 % marks of each practical course.

37

Algorithm 8 marks

Coding 10 marks

Key and execution 20 marks

Record 12 marks

-------- Total 50 marks

-------

The external viva voce examinations Research / project works also will

be conducted before the commencement of theory examinations. Under

exceptional conditions these examinations may be conducted after theory

examinations are over. The external assessment is for 60 % marks of the

project / research work / Dissertation.

The External Assessment mark for project evaluation is based on the

following criteria.

a) Assessment (80%) 96 b) Viva (20%) 24

------------------- Total Marks 120

-------------------

a) Assessment calculation (96 marks) a. Methodology 20 b. Application Skill / Tools & Techniques / Analysis 36

c. Logical Presentation & result / Future enhancement / Suggestion 20 d. Regularity with Punctuality 20

------------------- Total Marks 96

-------------------

End Semester Examination Question Paper Pattern Syllabus : All Five Units Working Days : On completion of a minimum of 90 working days.

Duration : Three Hours Max. Marks : 75


For the End semester external theory examinations, the question paper pattern shall be the same for all UG and PG programs, as given below, except in the case of Part – II English.

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Section A

Attempt all questions 10 questions – each carrying one mark 10 X 01 = 10

No Choice Section B

Attempt all questions

05 questions – each carrying five marks 05 X 05 = 25 Inbuilt Choice [Either / Or]

Section C

Attempt all questions 05 questions – each carrying eight marks 05 X 08 = 40 Inbuilt Choice [Either / Or]

4. Essential conditions for the Award of Degree / Diploma / Certificates:

1. Pass in all components of the degree, i.e., Part–I, Part–II, Part–III, Part – IV and Part–V individually is essential for the award of degree.

2. First class with Distinction and above will be awarded for part III only. Ranking will be based on marks obtained in Part – III only.

3. GPA (Grade Point Average) will be calculated every semester separately. If a candidate has arrears in a course, then GPA for that particular course will not be calculated. The CGPA will be calculated for those candidates who have no arrears at all. The ranking also will be done for those candidates without arrears only.

4. The improvement marks will not be taken for calculating the rank. In the case of courses which lead to extra credits also, they will neither be considered essential for passing the degree nor will be included for computing ranking, GPA, CGPA etc.

5. The grading will be awarded for the total marks of each course.

6. Fees shall be paid for all arrears courses compulsorily.

7. There is provision for re-totaling and revaluation for UG and PG programmes on payment of prescribed fees.

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5. Classification of Successful Candidates [Course-wise]

RANGE OF MARKS (In percent)

GRADE POINTS GRADE DESCRIPTION

90 - 100 9.0 - 10.0 O OUTSTANDING

80 - 89 8.0 - 8.9 D+ EXCELLENT

75 - 79 7.5 - 7.9 D DISTINCTION

70 – 74 7.0 - 7.4 A+ VERY GOOD

60 – 69 6.0 - 6.9 A GOOD

50 – 59 5.0 - 5.9 B AVERAGE

40 – 49 # 4.0 - 4.9 C SATISFACTORY

00 – 39 0.0 U RE-APPEAR

ABSENT 0.0 U ABSENT

Reappearance is necessary for those who score below 50% Marks in PG **;

those who score below 40% Marks in UG*; # only applicable for UG programs

Individual Courses

Ci= Credits earned for course “i” in any semester Gi= Grade Point obtained for course “I” in any semester

'n' refers to the semester in which such courses were credited.

GRADE POINT AVERAGE [GPA] = ΣCi G i

ΣCi Sum of the multiplication of grade points by the credits of the courses

GPA = ---------------------------------------------------------------------------------------

Sum of the credits of the courses in a semester

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Classification of Successful Candidates:

CGPA GRADE CLASSIFICATION OF FINAL RESULT

9.5 to 10.0 O+ First Class - Exemplary *

9.0 and above but below 9.5 O

8.5 and above but below 9.0 D++

First Class with Distinction * 8.0 and above but below 8.5 D+

7.5 and above but below 8.0 D

7.0 and above but below 7.5 A++

First Class 6.5 and above but below 7.0 A+

6.0 and above but below 6.5 A

5.5 and above but below 6.0 B+ Second Class

5.0 and above but below 5.5 B

4.5 and above but below 5.0 C+ # Third Class

4.0 and above but below 4.5 C #

0.0 and above but below 4.0 U Re-appear

“*” The candidates who have passed in the first appearance and within the prescribed semester ofthe

Programme (Major, Allied and Elective Course alone) are eligible.

“#” Only applicable to U.G. Programme

ΣnΣiCniGni

CUMULATIVE GRADE POINT AVERAGE [CGPA] = ------------------ ΣnΣiCni

Sum of the multiplication of grade points by the credits of entire program

CGPA=----------------------------------------------------------------------------------- Sum of the Courses of entire Program

41

In order to get through the examination, each student has to earn the

minimum marks prescribed in the internal (wherever applicable) and external

examinations in each of the theory course, practical course and project viva.

Normally, the ratio between internal and external marks is 25:75. There is

no passing minimum for internal component. The following are the minimum

percentage and marks for passing of each course, at UG and PG levels for external

and aggregate is as follows:

S.No Program Passing Minimum in Percent

External (75) Aggregate (100)

1 UG Degree 40% (30) 40% (40)

2 PG Degree 50% (38) 50% (50)

However, the passing minimum marks may vary depending up on the

maximum marks of each course. The passing minimum at different levels of marks is given in the following table:

S.No

UG & PG Maximum Marks

Passing minimum for UG Passing minimum for PG

Int. Ext. Total Int. Ext. Agg. 40% Int. Ext. Agg. 50%

1 25 75 100 - 30 40 - 38 50

2 50 150 200 - 60 80 - 75 100

3 40 60 100 - 24 40 - 30 50

4 80 120 200 - 48 80 - 60 100

5 80 20 100 - 8 40 - 10 50

6 160 40 200 - 16 80 - 20 100

7 15 60 75 - 24 30 - 30 38

8 50 - 50 20 - 20 25 - 25

9 - 50 50 - 20 20 - 25 25

10 - - 100 - - - - 50 50

11 20 30 50 - - - - 15 25

12 - - 200 - - - - 100 100

13 10 40 50 - - - - 20 25 Reappearance

The students having arrears shall appear in the subsequent semester (external) examinations compulsorily. The candidates may be allowed to write the examination in the same syllabus for 3 years only. Thereafter, the candidates shall be permitted to write the examination in the revised / current syllabus depending on various administrative factors. There is no re-examination for internals.

42

Criteria for Ranking of Students:

1. Marks secured in all the courses will be considered for PG Programs and marks secured in core and allied courses (Part-III) will be considered for

UG programs, for ranking of students. 2. Candidate must have passed all courses prescribed chosen / opted in the

first attempt itself.

3. Improvement marks will not be considered for ranking but will be considered for classification.

4. External Examination Grievances Committee:

Those students who have grievances in connection with examinations may

represent their grievances, in writing, to the chairman of examination grievance committee in the prescribed proforma. The Principal will be chairman of this committee.

43

SREE SARASWATHI THYAGARAJA COLLEGE (AUTONOMOUS)

THIPPAMPATTI, POLLACHI - 642 107 Student Grievance Form

(Forms Available at Utility Stores) Date: Place:

From Register No : ………………………………………........, Name : ………………………………………........,

Class : …………………………………………....., SreeSaraswathiThyagarajaCollege,

Pollachi – 642 107 To

The Principal / Examination-in-charge,

Sree Saraswathi Thyagaraja College, Pollachi – 642 107

Through: 1. Head of the Department,

Department of ……………….……….,


2. Dean of the Department Faculty of ……………………………….,


Respected Sir / Madam, Sub: ………………………………………………………………………. - reg.

NATURE OF GRIEVANCE… …………………………………………………………………………………………………

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

Thanking you, Yours Truly,

Signature

Forwarded by:

1. HOD with comments / recommendation ………………………………………………………………………………………............ 2. Dean with comments / recommendation

………………………………………………………………………………………............. 3. Signature and Directions of the Principal

………………………………………………………………………………………............. 4. Controller of Examinations: ………………………………………………………………………………………….………

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