MATH 225 Calculus IIISouth Dakota School of Mines & Technology

Fall 2016

Section 03: MTWF 1:00pm-1:50pm McLaury 313Section 07: MTWF 4:00pm-4:50pm McLaury 306

Instructor: Brent Deschamp

Email: brent.deschamp@sdsmt.edu

Website: http://webpages.sdsmt.edu/∼bdescham

Office: McLaury 316B

Phone: 605-394-2476

Office Hours:

Monday 3-4pm

Tuesday 2-3pm

Wednesday 11am-12pm

Thursday

Friday 10-11am

And by appointment

Text: Thomas’ Calculus, Thirteenth Edition by George Thomas, Maurice Weir, and Joel Haas

Course Description: A continuation of the study of calculus, including an introduction to vectors,vector calculus, partial derivatives, and multiple integrals. 4 credits.

Objectives: A student who successfully completes this course should be able to:

1. Analyze position, velocity, and acceleration in two or three dimensions using the calculus ofvector-valued functions.

2. Use partial derivatives to calculate rates of change of multivariate functions.

3. Use multiple integrals to compute the volume, mass, center of mass, and related quantitiesfor multivariate functions.

4. Compute line integrals, including those representing work done by a variable force in a vectorfield.

Grading:

Exam 1 20% Exam 2 20%

Exam 3 20% Exam 4 20%

Exam 5 20%

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In order to pass the course, students must pass an Integration Gateway. Each Gateway will consistof seven integration problems, and a student must correctly answer at least five questions in orderto pass. Any student who does not pass the Gateway will receive an F for the course. Gatewayswill be administered outside of class, and students must pass the Gateway before the first exam.The required knowledge for the Gateway can be found on a later page of this syllabus.

Most Wednesdays will be reserved for exams and no lecture will take place. See the schedule laterin this syllabus for exams days. Students must take Exams 1–5 in numerical order, but they cantake any exam on any available Wednesday. Students must sign up for an exam on Tuesday, inperson and in class. Electronic sign ups will not be accepted. In order to pass an exam a studentmust pass each problem on the exam with at least a C. Any problems not passed must be passedbefore the student can take the next exam. A student is not required to complete every problemon an exam when they sign up for an exam, but they will need to pass each problem before theymove on to the next exam.

If a student attempts a problem and does not pass it, then they will be required to come to myoffice in person and justify why a second attempt should be given. Justification will include, ata minimum, evidence of homework and the correction of the previous attempt. Any subsequentattempts will only focus on those problems not passed on the previous attempt, though anyshort-answer questions will be answered on every attempt. Whatever grade is assigned for theshort-answer questions on the final attempt of an exam will be the score for that problem. Also,signing up for an exam and not showing up for the exam will be considered an attempt, andjustification will be needed before a student can sign up for the exam again.

When a student receives a passing grade on a problem, then that will be the final grade enteredinto the grade book. So, if you want an A or B on a problem, then you must earn that gradeon your first attempt. This is being implemented so that students are not repeatedly taking oneexam in an attempt to improve their grade, which will occur at the expense of passing futureexams.1 The scheduled time for the final exam will be used as follows: (1) Any student who has passedevery question on every exam with at least a C or better is excused from the final testing period.(2) Any student who has not passed every question on every exam with a C or better, and is stillactive in the course, is required to come to the final exam period and to attempt any remainingproblems, unless the number of problems remaining is so numerous that further attempts precludethe student from passing the course. (3) Any student who does not come to the final testingperiod and attempt any remaining problems will receive a zero on those remaining problems, aswell as any short-answer questions for that exam, since short-answer must be answered on everyexam. (4) Since the final-exam period is the last scheduled date for the course, then any scoreearned during the final-exam period will constitute the grade for that exam. This policy is inkeeping with the spirit of the testing program, which is to remind students that the goal of thecourse is to master the material and not merely accumulate enough points to pass the course.

The Final Exam is scheduled for Thursday, December 8, 7-8:50am, though that time will not befor a designated final exam but will be the last available time for exams.

A grade of D will not be assigned as a course grade. Any student not earning at least a C will beassigned an F for the course.

1This paragraph was added on December 8, 2016 in order to clarify questions concerning the final-exam testingperiod.

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The following system will be used when grading exam problems. Points may be deducted untilno more points are left to deduct. Note that this means that while the procedure may be correct,no points could be awarded for a given problem because of poor computational skills. Additionalpoints may be taken off if a given mistake radically changes the nature or complexity of theproblem.

Point(s) off Error

1 Arithmetic and minor Algebra errors, not writing out a u-substitution2 Major Algebra and all Calculus errors3 Loss of a +C with an indefinite integralall Errors listed later as The Deadly Sins of Mathematics

Homework: Homework will be assigned regularly, but will not be collected. Assignments will be short,but will cover the material presented. Homework is a learning tool. If exam scores are low, it isan indication that more homework should be done beyond what is assigned.

Academic Integrity: According to the Undergraduate Catalog, “The consequences for any act ofacademic dishonesty shall be at the discretion of the instructor of record, subject to due processas outlined in BOR policy 3.4.3A. Sanctions may range from requiring the student to repeat thework in question to failure in the course.” For the purpose of this course, any student caughtcheating will receive an F in the course.

Technology: Maple will be required. All computers are banned from the classroom. This is a conse-quence of past problems, and this decision has been made in order to improve student performance.

Freedom in Learning: Under Board of Regents and University policy student academic performancemay be evaluated solely on an academic basis, not on opinions or conduct in matters unrelatedto academic standards. Students should be free to take reasoned exception to the data or viewsoffered in any course of study and to reserve judgment about matters of opinion, but they areresponsible for learning the content of any course of study for which they are enrolled. Studentswho believe that an academic evaluation reflects prejudiced or capricious consideration of studentopinions or conduct unrelated to academic standards should contact the dean of the college whichoffers the class to initiate a review of the evaluation.

Help: I am here to make sure you learn and understand the material. It is your job to let me knowwhen you are having difficulties. I will be glad to work around your schedule to help you.

Students with special needs or requiring special accommodations should contact the instructor,(your name, at your number) and/or the Director of Counseling and Disability Services, Ms.Megan Reder-Schopp, at megan.reder-schopp@sdsmt.edu or 394-6988 at the earliest opportunity.

All of this is subject to change.

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The Deadly Sins of Mathematics(Adapted from Dr. Kowalski)

Committing a deadly sin on any problem will result in a score of 0.

1. False Distribution

Thou shalt no distribute (or factor) anything across a sum (or difference), except multiplication.

� ab+c 6=

ab +

ac

a+bc = a

c +bc

� (a+ b)c 6= ac + bc

– Ex1: (x+ 2)2 6= x2 + 22

(x+ 2)2 = x2 + 4x+ 4

– Ex2:√t+ 5 6=

√t+√5

� sin (a+ b) 6= sin a+ sin b

� ea+b 6= ea + eb

� log (a+ b) 6= log a+ log b

log (ab) = log a+ log b

2. False Cancellation

Thou shalt not cancel any expression from a fraction, except common factors found after thouhast factored first.

� ax+ba 6= x+ b

� sin asin b 6=

ab

� ln aln b 6=

ab

3. False Products

Thou shalt not differentiate any product (or quotient, or composition) factor-by-factor.

� ddx (f(x)g(x)) 6=

dfdx ·

dgdx

�

∫f(x) · g(x) dx 6=

(∫f(x) dx

)·(∫

g(x) dx

)� (f ◦ g)(x) 6= f(x)g(x)

(f ◦ g)(x) = f(g(x))ddx ((f ◦ g)(x)) 6=

dfdx ·

dgdx

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4. Trignorance

Thou shalt not plead ignorance of trigonometric (or inverse trigonometric) functions at standardvalues. Thou shalt also know the standard trigonometric and inverse trigonometric derivatives(sin−1 (x) and tan−1 (x)) and integrals.

� cos (2x)·2 6= cos (4x)

� tan−1(x) 6= cotx

(tanx)−1 = cotx

� ddx(sec (2x)) 6= sec · tan (2x)ddx(sec (2x)) = 2 sec (2x)· tan (2x)

5. Other common sins

� ln 0 6= 0

ln 1 = 0

� ea ln b 6= ab

ea ln b = eln ba = ba

�√−9 6= 3√−9 = 3i

�

∫ln (x) dx 6= 1

x

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MATH 225 Calculus IIIIntegration Gateway topics

Know derivatives, Product Rule, and Chain Rule from Calculus I.

Know the following integrals.∫un du =

un+1

n+ 1+ C

∫1

udu = ln |u|+ C∫

eu du = eu + C

∫au du =

1

ln aau + C

d

du(loga u) =

1

u ln a∫sinu du = − cosu+ C

∫cosu du = sinu+ C

∫sec2 u du = tanu+ C∫

csc2 u du = − cotu+ C

∫secu tanu du = secu+ C

∫cscu cotu du = − cscu+ C∫

1

1 + u2du = tan−1 u+ C

∫1√

1− u2du = sin−1 u+ C

Be able to solve the following using a w-substitution.∫tanu du

∫cotu du

w = cosu w = sinu

Be able to solve the following using the correct trigonometric identity.∫sin2 u du

∫cos2 u du

sin2 u = 12 (1− cos (2u)) cos2 u = 1

2 (1 + cos (2u))

Know the following techniques.

u-substitution Integration by Parts

Be able to recognize unsolvable integrals.

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MATH 225 Calculus IIIReading Assignments/Schedule

Monday Tuesday Wednesday Friday

8/22: §11.1 8/23: §11.2 8/24: §11.2, §11.3 8/26: §11.3

8/29: §11.5 8/30: §12.1,2,3,4 8/31: §12.5 9/2: §12.5

9/5: No class 9/6: §12.6 9/7: §12.6 9/9: §13.1

9/12: §13.2, §13.3 9/13: §13.4 9/14: Exam 1 9/16: §13.4, §13.5

9/19: §13.5 9/20: §14.1 9/21: 9/23: §14.3

9/26: §14.4 9/27: §14.5 9/28: Exam 2 9/30: No class

10/3: §14.7 10/4: §15.1 10/5: 10/7: §15.2

10/10: No class 10/11: §15.2 10/12: Exam 3 10/14: §15.4

10/17: §15.4 10/18: §15.5 10/19: 10/21: §15.5

10/24: §15.7 10/25: §15.7 10/26: 10/28: §15.8

10/31: §15.8 11/1: §16.1 11/2: Exam 4 11/4: §16.2

11/7: §16.2 11/8: §16.3 11/9: 11/11: No class

11/14: §16.3 11/15: §16.4 11/16: 11/18: §16.4

11/21: §16.4 11/22: 11/23: No class 11/25: No class

11/28: §16.6 11/29: §16.6 11/30: 12/2: §16.6

12/5: §16.7 12/6: §16.8 12/7: No class 12/9: Finals

12/12: Finals 12/13: Finals 12/14: Finals 12/16:

Note that the final exam is on Thursday, December 8, which is not on this calendar.

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MATH 225 Calculus IIIHomework Assignments (Thomas, 13th Edition)

Section Page Problems

11.1 Parametrizations of Plane Curves 641 1–8

11.2 Calculus with Parametric Curves 649 1,5,9,25–30

11.3 Polar Coordinates 659 1,6,7,11–16,27–34,47–50,53–60

11.5 Areas and Lengths in Polar Coordinates 667 1–4,11–14,21–23

12.2 Vectors 697 1–8,9,12,13

12.3 The Dot Product 706 1–8 (a) and (b) only

12.4 The Cross Product 714 1–8,27,28

12.5 Lines and Planes in Space 720 1,2,8,23,27,29

12.6 Cylinders and Quadric Surfaces 728 1–12,14,17,21,27

Exam 1

13.1 Curves in Space and Their Tangents 739 9–11,19

13.2 Integrals of Vector Functions 747 1,3,4,11,14

13.3 Arc Length in Space 756 1–4,9–13

13.4 Curvature and Normal Vectors of a Curve 760 1–4,9–11,21

13.5 Tangential and Normal Components of Acceleration 766 1–4,7,8–11,17–20

Exam 2

14.1 Functions of Two or More Variables 781 1,5,7,13,15,31–36,49–52

14.3 Partial Derivatives 798 1–18,41–50,65,66,75,83,90

14.4 The Chain Rule 809 7,8,11–16,25,26,44,45

14.5 Directional Derivatives and Gradient Vectors 818 1–4,11–13,19–21,25–28,29

14.7 Extreme Values and Saddle Points 836 1–8,31–33,57–59

Exam 3

15.1 Double and Iterated Integrals over Rectangles 870 1–8,10,20–22

15.2 Double Integrals over General Regions 875 9–12,19–24,29–36,47–54

15.4 Double Integrals in Polar Form 888 1–26

15.5 Triple Integrals in Rectangular Coordinates 894 7–32,41–44

15.7 Triple Integrals in Cylindrical and Spherical Coordinates 910 1–10,15–18,21–30,33–38

15.8 Substitutions in Multiple Integrals 922 1,3,6,7,9,13,14,16,21,22

Exam 4

16.1 Line Integrals 938 1–16,25

16.2 Vector Fields and Line Integrals 945 1–4,7–16,19–24

16.3 Path Independence, Conservative Vector Fields 957 1–4,7–10,18–22,25,30

16.4 Green’s Theorem in the Plane 968 5–12,19–24

16.6 Surface Integrals 996 1–8,13–17,19–28

16.7 Stoke’s Theorem 1002 1–6,13–18

16.8 The Divergence Theorem 1015 5–10

Exam 5

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