Syllabus Detail

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 Variables

Approved: 2003-10-01 (revised 2022-06-02, J.Hunter, J. Schultens, and B. Temple)
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Complex Variables and Applications, Ninth Edition by James Brown and Ruel V. Churchill; McGraw Hill Publisher
Search by ISBN on Amazon: 978-0073383170
Prerequisites:
MAT 185A
Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-2

Chapter 7 (pages 259-273)

Evaluation of Improper Integrals

3

Chapter 7 (pages 174-183)

Integration along a Branch Cut

4

Chapter 7 (pages 187-193)

Argument Principle and Rouche's Theorem

5

Chapter 7 (pages 194-198)

Inverse Laplace Transform

6-7

Chapter 8 (pages 299-309)

Linear Fractional Transformations

8-9

Chapter 8 (pages 313-331)

Mappings of the Upper Half Plane

10-11

Chapter 8 (pages 338-344)

Riemann Surfaces

12-14

Chapter 9

Conformal Mapping

15-16

Select examples from Chapter 10

Applications of Conformal Mappings

17-18

Select examples from Chapter 11

The Schwarz-Christoffel Transformation

19-21

Chapter 12

Integral Formulas of the Poisson Type

22-24

Other sources

Asymptotic Expansions and the Method of Steepest Descent

25-27

Other sources

Applications of the Laplace Transform

Learning Goals:
AS A CAPSTONE: Students will broaden their study of complex analysis in this second course of the MAT 185 sequence. They will learn about connections between complex analysis and geometry/topology, and also study techniques such as asymptotic expansions and the Laplace transform that are central in the analysis of differential equations. Students will gain mastery over such far-reaching applications of complex analysis, and develop their ability to communicate at a capstone level, commensurate with that expected of an undergraduate degree in mathematics.