MATH 660 -- Complex Analysis

This is an introductory course in complex analysis of one variable. Topics include: linear transformations, analytic functions, conformal mappings, Cauchy's theorem and applications, power series, partial fractions and factorization, elementary Riemann surfaces, Riemann's mapping theorem. MATH 410 or equivalent is a prerequisite for this course.

Here is some more basic information about MATH 660:

Time & Place:

 MWF 11:00-11:50 am, HBK 0103

Instructor:

Professor Richard A. Wentworth
Office: 3109 Mathematics Building
Phone: (301) 405-5130
Office Hours: MW 9:30-10:30 am, and by appointment
Email: raw@umd.edu
Web: www.math.umd.edu/~raw

Text:

Complex Analysis, by Theodore W. Gamelin, Springer.
Also recommended: Complex Analysis, by Lars Ahlfors, McGraw Hill.

Homework:

There will be 11 homework assignments (the lowest score will be dropped). In addition, you should work through the problems in the text, since they are typical of the types of problems that will appear on the exams.

Exams:

There will be a midterm exam in class on March 13 and a final exam in class on May 8.

Grading:

The final grade will depend on your performance on the exams and homework. The midterm exam, the final exam, and the homework are each worth 100 points.

Detailed Syllabus:

Below is an outline of the material I hope to cover. This will change often as the semester progresses, so check here often for updates. The reading selections are from Gamelin.

WEEK

DATE

TOPICS

READING

HOMEWORK ASSIGNMENTS

1

Jan 23

Introduction. Basics.

Ch. 1

2

Jan 28

Analytic functions.

Ch. 2

3

Feb 4

Integrals. Harmonic functions.

3.1-5

4

Feb 11

Cauchy's theorem.

Ch. 4

5

Feb 18

Integral formulas. Power series.

Ch. 5

6

Feb 25

Laurent series. Singularities

6.1-4

7

Mar 4

Winding number and residue theorem.

7.1-4

8

Mar 11

Review. Midterm exam.

--

9

Mar 25

Applications of the residue theorem.

10

Apr 1

The Argument Principle and Rouche's theorem.

Ch. 8 (omit 8.5, 8.7)

11

Apr 8

Schwarz lemma.

Ch. 9

12

Apr 15

Harmonic functions.

Ch. 10

13

Apr 22

Riemann mapping theorem.

Ch. 11 (omit 11.4)

14

Apr 29

Prime number theorem.

Ch. 14

15

May 6

Review. Final exam.

--

Richard A. Wentworth