**MATH 428: Complex Variables**

**Three hours lecture (3)**

**Prerequesite: MATH 271**

A study of elementary functions with complex domain and techniques of differentiation
and integration of complex functions., including the Cauchy Riemann equations, line
integrals and Cauchy's Integral Formula.

Detailed Description of Content of Course

The following topics in complex variables will be covered:

1) The complex number system

2) Limits and continuity for functions of a complex variable

3) Differentiability and the Cauchy-Riemann equations

4) Properties of elementary functions

5) Line integrals and Cauchy's Integral Theorem

6) Cauchy's Integral Forumla and its applications.

Time permitting the following topics may be covered: Laurent series, The Residue Theorem,
Conformal Mappings, Fourier Transform

Detailed Description of Conduct of Course

Most instructors will use the lecture method and will require students to work problems
assigned as homework. Some instructors may use mathematical software**.**

Goals and Objectives of the Course

The student is expected to gain a knowledge base and problem solving skills in complex
variables.

Assessment Measures

Graded tasks may include tests, quizzes, homework, class participation and attendance.

Other Course Information

This course is intended for students in mathematics, the physical sciences or in computer
science.

Review and Approval

November 7, 2017

March 30, 2016

Sept. 2001 Review Stephen Corwin, Chair