Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 185B: Complex Analysis
Approved: 2003-10-01, D. Coutand & B. Nachtergaele

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Basic Complex Analysis, Marsden & Hoffman, 3rd edition ($122)
Search by ISBN on Amazon: 0-7167-2877-X

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-2

5.1

Basic theory of conformal mappings

3-4

5.2

Fractional linear transformations

5-7

5.3

Applications of conformal mappings

8-10

6.1

Analytic continuations and Riemann surfaces

11-12

6.2

Rouche’s Thm and Principle of the Argument

13-14

6.3

Mapping properties of analytic functions

15-17

7.1

Infinite products and the Gamma function

18-20

7.2

Asymptotic expansions and the Method of Steepest Descent

21-22

7.3

Stirling’s formula etc.

23-24

8.1

Basic properties of the Laplace Transform

25

8.2

Complex Inversion Formula

26-27

8.3

Applications of the Laplace Transform

Additional Notes:

Chapters 5-8