Syllabus 185A: Complex Variables
Winter 2004

Lectures: MWF 9:00-9:50pm, Wellman 7
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371, anne@math.ucdavis.edu
Office hours: M 10-11am, F 11-12am or by appointment
T.A.: Philip Sternberg, Kerr Hall 565, sternberg@math.ucdavis.edu
Office hours: Tuesday 10-11am
Text: The recommended book for the class is
  • J.E. Marsden, M.J. Hoffman, Basic complex analysis, 3rd edition, ISBN 0-7167-2877-X, published by Freeman and Company.
However, I will not require students to purchase the book. Other good texts are
  • Serge Lang, Complex Analysis (especially if you want to go on to graduate school in mathematics)
  • E.B. Saff, A.D. Snider, Fundamentals of complex analysis for mathematics, science and engineering (easier text, sometimes not completely mathematically rigorous)
Problem Sets: There will be weekly homework assignments, handed out on Wednesday, due the following Wednesday.
You are encouraged to discuss the homework problems with other students. However, the homeworks that you hand in should reflect your own understanding of the material. You are NOT allowed to copy solutions from other students or other sources. If you need help with the problems, come to office hours! The best way to learn mathematics is by working with it yourself. No late homeworks will be accepted.
Exams: There will be one Midterm held in class on February 13 and a comprehensive Final Exam on March 18 at 10:30am.
There will be no make-up exams!
Grading: The final grade will be based on: Problem sets 25%, Midterm 25%, Final 50%
Web: http://www.math.ucdavis.edu/~anne/WQ2004/185A.html

Course description

This course is the first part of a two-quarter introduction to the Theory of Complex Functions. The class is primarily based on Chapters 1-4 of the book by Marsden and Hoffman.

1. Analytic functions
Introduction to complex numbers, complex powers, topology of the complex plane, complex functions and limits, elementary functions, analyticity and the Cauchy Riemann relations

2. Cauchy's theorem
contour integration and Cauchy's theorem, harmonic functions

3. Series representation of analytic functions
convergent series of analytic functions, Laurent and Taylor series, zeroes and singularities

4. Calculus of residues
calculation of residues, residue theorem

Problem sets

Homework 0: Send me an e-mail at anne@math.ucdavis.edu and tell me something about yourself, what kind of math you like, what you expect of the class or anything else, so that I can get to know you all a little bit!

Homework 1: due January 21, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 2: due January 28, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 3: due February 4, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 4: due February 11, 2004 in class: ps or pdf
Solutions: ps or pdf

Homework 5: due February 18, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 6: due February 25, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 7: due March 3, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf

Homework 8: due Friday (!!) March 12, 2004 in class: ps or pdf
Solutions by Philip: ps or pdf
anne@math.ucdavis.edu