Math CS-120: Multivariate Analysis II: Integration
Fall 2010
Review Problems
Syllabus
Instructor:
Helena McGahagan
Office: South Hall, Room 6507
Email:
helena-A.T.-math.ucsb.edu
Lectures: TR, 10:00am-12:20pm, 494 164B
Office Hours:
I have scheduled Wed. 12:30-1:30 as a regular office hour for this class.
I am also happy to schedule office hours by appointment as needed.
If needed, we can use the last 15 or so minutes of class as additional
office hours for any short questions you may have.
[I have also scheduled office hours for my other classes at Mon.
9-noon
and Wed. 9-noon. You are welcome to drop by any of those times;
if the office hours are not too busy, I can meet with you then.]
Textbook: Advanced Calculus of Several Variables,
C.H. Edwards, Jr.
Other references include Multidimensional Real Analysis II:
Integration by Duistermaat and Kolk;
Mathematical Analysis by Apostol; and Calculus on Manifolds
by Spivak.
Course Description:
This is the second part of a two-quarter sequence on Multidimensional
Analysis. This course focuses on integration, and will cover most of
Chapters IV
and V in your textbook. We will begin, however, with a detailed review of
integration in
one variable before generalizing to multiple dimensions.
After this, the course will
present the main ideas of multiple integration: Volume and the
n-dimensional
integral, Riemann sums, iterated integrals and Fubini's theorem, the
change of
variables theorem, and improper integrals. The second part of the course
will cover
differential forms and
the famous integral theorems of multivariate calculus: Green's theorem,
the divergence theorem,
and Stokes' theorem.
Homework:
There will be homework problems due in lecture; please check the course
website to
download problem sets. Discussion of the course and lecture material is
highly encouraged.
Although discussion of the homework and collaboration is
usually allowed, all homework problems turned in must be your own work and
reflect your own understanding of the problems. Occasionally, there may
be a problem set on which
collaboration is not allowed.
Attendance and Partcipation:
Attendance at all lectures is required. During the last half hour of
class (before the office hours),
students will be expected to discuss and occasionally present homework
problems.
Evaluation:
Students will be evaluated according to the following criteria: Regular
attendance, number of assignments completed and the quality
of the assignments, understanding of the mathematical material,
participation
in class, development of oral presentation and proof-writing skills,
and
effort.