Department
of Mathematics
Mathematics 107. Vector Calculus
Fall 2008
Course Outline
Time
and Place: MWF
10:00 am - 10:50 am Millikan 218
Instructor: Dr. Adolfo J. Rumbos
Office: Andrew 259
Phone / e-mail: ext. 18713
/
Office Hours: MWF 9:15 am-9:50 am or by
appointment
Text: Second Year
Calculus by David M. Bressoud
Undergraduate
Texts in Mathematics, Springer 2000
Prerequisites: Math
60 (Linear Algebra) or equivalent course.
Course
Description. The main goal of this course is the development
of differential and integral calculus ideas, which students learned in a
single-variable calculus courses, in dimensions higher than 1. The main objects of study are functions from n-dimensional Euclidean space to m-dimensional Euclidean space (also
known as Vector Fields) and their
differentiation and integration properties.
We will also be concerned with the study of subsets of Euclidean space
on which those functions act. The
culmination of the course will be the multivariable version of the Fundamental Theorem of Calculus (also
known as the generalized Stokes’ Theorem). In the process leading to Stokes’ Theorem,
the machinery of differentiable
manifolds and differential forms
will be introduced and developed.
The
specific topics to be covered are listed in the attached Tentative Schedule of Lectures and Examinations.
Assigned
Grading
Policy. Grades will be based on the homework, two
50-minute examinations, plus a comprehensive final examination. The grades will be computed as follows:
homework
20%
Two 50-minute
exams 50%
final examination 30%
Final
Examination.
Time: Wednesday,
December 17 9:00 am
Place: Millikan
218
Math 107 Fall
2008
Tentative Schedule of Lectures and
Examinations
Date Topic
W Sep.
3 n-Dimensional
Euclidean Space
F Sep. 5 Spans,
lines and planes
M Sep. 8 Dot product and Euclidean norm
W Sep.
10 Orthogonality and projections
F Sep.
12 The cross product
M Sep. 15 Functions
on Euclidean space
W Sep.
17 Open subsets of
Euclidean space
F Sep.
19 Continuous functions
M Sep. 22 Continuous
functions (continued)
W Sep.
24 Limits and continuity
F Sep.
26 Differentiability
M Sep. 29 The
derivative map
W Oct.
1 The derivative map (continued)
F Oct.
3 Sufficient
conditions for differentiability
M Oct. 6 Sufficient
conditions for differentiability (continued)
W Oct.
8 Derivatives
of compositions
F Oct.
10 Derivatives of
compositions (continued)
M Oct. 13 Review
W Oct.
15 Exam 1
F Oct.
17 Problems and Examples
M Oct. 20 Fall
recess: No Classes
W Oct.
22 Path integrals
F Oct.
24 Path integrals
(continued)
M Oct. 27 Line
integrals
W Oct.
29 Gradient fields
F Oct.
31 Flux across plane
curves
M Nov. 3 Differential forms
W Nov.
5 Calculus of differential
forms
F Nov.
7 Calculus of differential
forms (continued)
Date Topic
M Nov. 10 Evaluating
2-forms: Double integrals
W Nov.
12 Green’s Theorem
F Nov.
14 Fundamental Theorem of
Calculus in two dimensions
M Nov. 17 Change
of variables Theorem
W Nov.
19 Change of variables
Theorem (continued)
F Nov.
21 Triple integrals
M Nov. 24 Surface
integrals
W Nov. 26 Stokes’
Theorem
F Nov.
28 Thanksgiving recess
M Dec. 1 Problems
and examples
W Dec.
3 Review
F Dec.
5 Exam 2
M Dec. 8 Review
W Dec.
10 Review
W Dec.
17 Final Examination