MATH 722: Analysis 2

Syllabus - Spring 2003

Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Office Hours: Mondays 10:30-11:20.

Textbook:
Main textbook: The Way of Analysis, (R. Strichartz), Revised Edition. Jones and Bartlett publisher.

In addition, I may occasionally use the following books:
1. Calculus on Manifolds (M. Spivak). (This is a little book worth owning!)
2. Functions of Several Variables (W. Fleming).
3. Analysis on Real and Complex Manifolds (R. Narasimhan).
These books are either in the library or in my office and can be borrowed if needed. I think the numbers rank them in
decreasing order of frequency of use.

Introduction to functions of several variables:

1. Limits and continuity of functions in several variables.
2. Derivative, tangent plane. Partial derivatives.
3. Maxima and minima. Lagrange multipliers.
4. Inverse function theorem.
5. Implicit function theorem.
6. Integration - multiple and iterated.
7. Fubini's theorem.
8. Jacobiand and change of variable.
9. Differential forms.
10. Closed forms, exact forms, Poincare' lemma.
11. Stokes' theorem.

Grading policy:

You must show all of your work in exams and homework in order to receive full credit.

1. Homework counts as 50% of the final grade. Homework will be assigned weekly, and will be due Mondays at 4:00 in the assigned
mailbox. Late homework will not be accepted.
2. A 50-minute midterm exam will count as 20% of the final grade.
3. The final will count as 30% of the final grade.

Journal

Here I keep track of the material we cover class by class, the exercises I assign, and the book I used.