Math 5C - Vector Calculus II - Winter 2007

Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: T 2 - 4, Th 1 - 3

Prerequisites: Math 5B (with a grade of C or better).

Text: Wilfred Kaplan.  Advanced Calculus.  Fifth edition, Addison-Wesley.

Lecture: T Th 9:30 - 10:45 am in 1006 North Hall.

Section: You must sign up for and attend a discussion section as well.  The section times and locations for this course are as follows: 

The GSI for this course is Garrett Johnson.  His office hours are:





Course Timetable (subject to change)




    Homework  (in Kaplan)

    Due Date    

Tu 1/9

Line Integrals in 2D and 3D,
Path Independence

Ch. 5.8 (review 5.1-5.6)

p. 312:  Ex. 1


Th 1/11

Triple Integrals, Cylindrical & Spherical Coordinates.

Lecture  Notes

p. 121: Ex. 6a
2 additional prob.s

Tu 1/16

Parametrized Surfaces, Orientability, Surface Area

Ch. 5.9, 4.7

p. 248: Ex. 3


Th 1/18

Surface Integrals of Functions and Vector Fields, Flux

Ch. 5.10

p. 313: Ex. 6a,b,d, 7a,b

Tu 1/23

Divergence Theorem

Ch. 5.11

p. 319:  Ex. 1a-e,  2a,c



Th 1/25

Stokes' Theorem

Ch. 5.12

p. 330:  Ex. 1, 3

Tu 1/30

Path Independence

Ch. 5.13
Lecture Notes

p. 330-1:  Ex. 2, 4


Th 2/1

Physical Applications

Ch. 5.15

Prob.s from Lecture

Tu 2/6

First Midterm

Ch. 5.8-5.13



Th 2/8

Infinite Sequences and Series, Limits.  Convergence, Divergence.

Ch. 6.1, 6.2, 6.5
Lecture Notes

Homework 5

Tu 2/13

Convergence & Divergence Tests: Geometric Series, nth Term Test, Integral Test, p-Series, Comparison Test.

Ch. 6.5-6.7

Lecture Notes

p. 396:  Ex. 1-4, 5a, 9b


Th 2/15

Alternating Series Test.  Absolute Convergence.  Ratio and Root Tests, Operations on Series.

Ch. 6.6, 6.7, 6.10
Lecture Notes

p. 396-7:  Ex. 6a, 7a, 8,  12a-f

Tu 2/20

Power Series.  Taylor & Maclaurin Series.

Ch. 6.11,  6.15-6.16
Lecture Notes

p. 417:  Ex. 1a,b,g,i



Th 2/22

Operations on Power Series.  Taylor Series for ArcTan x, sin x, cos x, (1+x)^.5

Ch. 6.15,6.17
Lecture Notes

p. 429:  Ex. 1, 3a,c,d, 4

Tu 2/27

Taylor's Formula with Remainder.  Series of Functions.  Uniform Convergence, M-Test.

Ch. 6.11-6.14
Lecture Notes

p. 417-8:  Ex. 1c,e,f, 2a,c,d,f


Th 3/1

Second Midterm

Ch. 6.1, 6.2, 6.4-6.7, 6.11, 6.15-6.17


Tu 3/6

Trigonometric & Fourier Series.  Fourier Coefficients.  Convergence Theorem.

Ch. 7.1 - 7.4
Lecture Notes

p. 478-9:  Ex. 1a,b,e,f, 5, 6



Th 3/8

(Differentiation &) Integration of Fourier Series.  Complex Form of Fourier Series.

Ch. 7.5, 7.17
Lecture Notes

Tu 3/13

Wave Equation.  General Solution.  Fourier Sine Series.

Ch. 10.7, 7.5
Lecture Notes



Th 3/15

Wave Equation (cont.).  Review.

Ch. 10.8

Lecture Notes


W 3/21

Final Exam - 8:00 - 11:00 am




Homework:  Homework exercises will be assigned in lecture and listed on the course webpage (sometimes in advance).  All homework problems assigned in a given week are due on the following Wednesday in section.  You may work together on homework problems; however, you must write up your answers individually.  You must show all your work in order to recieve full credit.  Late homeworks will not be accepted.  However, your lowest homework score will be automatically dropped.

Exams: There will be two in-class midterm exams on Tuesday February 6 and on Thursday March 1 from 9:30 to 10:45 am.  Please arrive promptly.  The final exam will be Wednesday March 21, 8:00 - 11:00 am.  The problems on the exams will closely resemble those on the homeworks.   No make-up exams will be given, except in extaordinary circumstances.  If you have a serious conflict with any of these exams or miss one for any reason, it is your responsibility to notify me immediately so that other arrangements may be made.

  Grades will be computed from your scores on homeworks and exams as follows: Homework = 20%, Each Midterm = 20%, Final = 40%.  No letter grades will be assigned until the end of the semester, and the exact grading scale will depend on the difficulty of the exams.  However,  a 90% or above will guarantee you at least an A, an 80% will be at least a B, and 70% will be at least a C.