Math 5B -
Vector Calculus
I - Fall 2006
Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: T
Office Hours for Finals' week: T 10-12, W
11-1, Th 1-4.
Prerequisites: Math 5A (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 Steve Read. His office hours are:
Announcements:
Class Schedule (subject to change) |
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Date |
Topics |
Reading |
Homework (in Kaplan) |
Due Date |
Th 9/28 |
Vectors, Dot Product, Cross Product, Lines |
Ch. 1.1-1.4 |
p. 15-16 : Ex. 2, 5, 6, 7 |
10/4 |
Tu 10/3 |
Planes, Functions of Several Variables, |
Ch. 2.1-2.3 |
p. 82 : Ex. 2, 3a,b |
10/11 |
Th 10/5 |
Limits, Continuity |
Ch. 2.4 |
p. 82 : Ex. 4, 5, 6 |
|
Tu 10/10 |
Partial Derivatives, Total Differential |
Ch. 2.5-2.6 |
p. 89-90 : Ex. 3, 4, 6 |
|
Th 10/12 |
Chain Rule, Jacobian Matrix |
Ch. 2.7-2.9 |
p. 95 : Ex. 1c,d,e, 2b, 3a,b |
|
Tu 10/17 |
Implicit Functions, Implicit Differentiation |
Ch. 2.10 (review Cramer's rule in Ch. 1.5) |
p. 104-105: Ex. 1b, 5, 6d |
10/25 |
Th 10/19 |
First Midterm Exam |
Ch. 1.2-1.4, 2.1-2.9 |
Exam + Solutions |
|
Tu 10/24 |
Cylindrical & Spherical Coordinates, |
Ch. 2.12, 2.13 |
p. 121: Ex. 1,2,3 |
|
Th 10/26 |
Tangent Planes, Gradient, |
Ch. 2.13, 2.14 |
p. 134-135: Ex. 1a,c,e |
|
Tu 10/31 |
Higher Order Derivatives, |
Ch. 2.15, 2.19 |
p. 142-143: Ex. 1c, 2a, 3 |
|
Th 11/2 |
Absolute Extrema, Lagrange Multipliers, |
Ch. 2.20, |
p. 158-159: Ex. 6b,c,e, 8b,c |
|
Tu 11/7 |
Vector and Scalar Fields, Gradient, |
Ch. 3.1-3.5 |
p. 180: Ex. 1a,b,c, 7 |
|
Th 11/9 |
Divergence, Curl, Combined Operations |
Ch. 3.6 |
p. 185: Ex. 3, 5, 7, 9 |
|
Tu 11/14 |
Review of Integration, Multiple Integrals |
Ch. 4.1,4.3,4.4 |
p. 234-5: Ex. 1a,b,c, 2a,c, 5 |
11/22 |
Th 11/16 |
Second Midterm Exam |
Ch. 2.10-2.20 (except 2.11, 17) |
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Tu 11/21 |
Triple Integrals, Change of Variables |
Ch. 4.6 |
p. 241-2: Ex. 4,7 |
11/29 |
Th 11/23 |
Thanksgiving holiday. No class. |
|
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Tu 11/28 |
Arc Length, Surface Area, |
Ch. 4.7, |
p. 278: Ex. 1,2 |
|
Th 11/30 |
Line Integrals |
Ch. 5.3-5.4 |
p. 279: Ex. 3,4 |
|
Tu 12/5 |
Green's Theorem |
Ch. 5.5 |
p. 286-7: Ex. 1, 5a-e, h |
|
Th 12/7 |
Independence of Path |
Ch. 5.6-5.7 |
p.300-1: Ex. 1, 2, 3a-d |
|
F 12/15 |
Final Exam - 8:00 - 11:00 am |
Ch. 1.1 - 5.6 |
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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 two lowest homework scores will be automatically dropped.
Exams: There will be two in-class midterm exams on Thursday
October
19 and on Thursday November 16 from 8:00 to 9:15 am.
Please
arrive promptly. The final exam will be Friday December 15,
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-.