MATH 721: Analysis I

Syllabus - Fall 2002

Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Office Hours: MW 8:30 - 9:20 a.m.

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.Principles of Mathematical Analyis (W. Rudin).
2. Introduction to Real Analysis (R. Bartle, D. Sherbert).
3. Analysis 1, 2, & 3 (O. Forster, these books are in German).
4. Analisis Matematico 1, 2, & 3 (Rey Pastor, Pi Calleja & Trejo, these books are in Spanish).
5. Analysis on Real and Complex Manifolds (R. Narasimhan).
6. Functions of Several Variables (W. Fleming).
7. Calculus on Manifolds (M. Spivak).
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 Real Analysis: Limits, continuity, uniform 

convergence, completeness, differentiation, Riemann integration.

1. Basics on the construction of the real numbers; completeness of the reals.
2. Complex numbers and arithmetic; complex exponentials and logarithms.
3. Introduction to metric spaces and topology.
4. Sequences and limits; series.
5. Limits of functions; continuity. Uniform continuity.
6. Cauchy sequences and completeness.
7. Convergence of sequences of functions: pointwise and uniform.
8. Convergence, equicontinuity, Arzela-Ascoli theorem.
9. Differentiation on the real line and in  C.
10. Mean value theorem, Taylor series.
11. Riemann integration.

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 every class meeting, and will be due the next Monday at 3:00 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.