Mathematics 428

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