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
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:
Announcements:
Course Timetable (subject to change) |
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Date |
Topics |
Reading |
Homework (in Kaplan) |
Due Date |
Tu 1/9 |
Line Integrals in 2D and 3D, |
Ch. 5.8 (review 5.1-5.6) |
p. 312: Ex. 1 |
|
Th 1/11 |
Triple Integrals, Cylindrical & Spherical Coordinates. |
p. 121: Ex. 6a |
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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 |
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Tu 1/30 |
Path Independence |
|
p. 330-1: Ex. 2, 4 |
|
Th 2/1 |
Physical Applications |
Ch. 5.15 |
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Tu 2/6 |
First Midterm |
Ch. 5.8-5.13 |
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|
Th 2/8 |
Infinite Sequences and Series, Limits. Convergence, Divergence. |
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Tu 2/13 |
Convergence & Divergence Tests: Geometric Series, nth Term Test, Integral Test, p-Series, Comparison Test. |
Ch. 6.5-6.7 |
p. 396: Ex. 1-4, 5a, 9b |
|
Th 2/15 |
Alternating Series Test. Absolute Convergence. Ratio and Root Tests, Operations on Series. |
|
p. 396-7: Ex. 6a, 7a, 8, 12a-f |
|
Tu 2/20 |
Power Series. Taylor & Maclaurin Series. |
|
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 |
|
p. 429: Ex. 1, 3a,c,d, 4 |
|
Tu 2/27 |
Taylor's Formula with Remainder. Series of Functions. Uniform Convergence, M-Test. |
|
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 |
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Tu 3/6 |
Trigonometric & Fourier Series. Fourier Coefficients. Convergence Theorem. |
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Th 3/8 |
(Differentiation &) Integration of Fourier Series. Complex Form of Fourier Series. |
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Tu 3/13 |
Wave Equation. General Solution. Fourier Sine Series. |
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Th 3/15 |
Wave Equation (cont.). Review. |
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W 3/21 |
Final Exam - 8:00 - 11:00 am |
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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: 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.