Mathematical Physics 212A
Fall 2003

Lectures. When: Tuesday & Thursday, 12:30pm-1:50pm. Where: RH 184
Discussions. When: Wednesday, 11:00am-11:50am. Where: RH 390

Instructor: Dr. Alexander (Sasha) Chernyshev, Assistant Professor
Office: FRH 2158
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/faculty/chernyshev.html

Introduction

This course is designed to give an introduction to some of mathematical methods used in physics.
Specifically, it deals with complex analysis and differential equations, common methods of evaluating integrals
and solving equations.

The prerequisite for the course is the knowledge of a real variable mathematical calculus.

The grade for the course will be based on: (i) homeworks (35%), due every Tuesday,
(ii) midterm (30%) [take-home],
(iii) and final exam (35%) [take-home].

Topics to be covered

Here is a list of topics I am planning to cover in the course. (Check the detailed Syllabus for the last year course below).

Functions of a complex variable (1/2 of the course)
- Complex numbers
- Analytic functions
- Contour integration
Asymptotic methods (1/6 of the course)
- Intergral representation methods (Laplace, steepest descent, stationary phase)
- Differential-equation methods (WKB)
Differential equations, Green's Functions (1/3 of the course)
- Ordinary differential equations
- Partial differential equations

Recommended Books

These books are all recommended but not required. They are available from the UCI bookstore.

G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a complex variable: Theorie and Technique, McGraw-Hill book company, New York, 1983.
This is an outstanding textbook on the complex analysis. It contains a big fraction of the topics I am going to discuss.

F. W. Byron and R. W. Fuller, Mathematics of classical and quantum physics, Dover Publications, Inc., New York, 1992.
Very good textbook on many different mathematical methods.

Other Books

G. B. Arfken, H. J. Weber, Mathematical methods for physicists, Academic press, London, 2001. [This is a comprehensive book on mathematical physics.]

G. Mahan, Applied Mathematics, Kluwer Academic/Plenum Publishers, New York, 2002. [Very good, practical book on complex analysis and differential equations.]