Math-460 Complex Variables with Application

Mathematics, Statistics & Computer Science Department

COURSE NO./TITLE: MATH-460 (355-460) COMPLEX VARIABLES WITH APPLICATION

CREDIT: 3

COURSE DESCRIPTION: Complex numbers, analytic functions, elementary functions of complex variables, mapping of elementary functions integration techniques, power series and calculus of residues.

Prerequisite: MATH-158.

TEXTBOOK:

  • Complex Variables & Applications, 7th Ed., by Brown/Churchill (adopted 1/04)
  • (Adopted 1/94: Basic Complex Variables, 2nd Ed., by Marsden)
    (Previously used: Complex Variables and Applications, 5th Ed., by Churchill)

COURSE OBJECTIVES:

  1. To develop students' reasoning and analytic abilities in general.
  2. To provide sound, rigorous understanding of function of a complex variable.
  3. To provide an introductory experience to the total field of analysis in mathematics through complementing the students' knowledge of real variables.
  4. To develop skill and appreciation in the many areas of application in the everyday world (electronics, mechanics, dynamics, hydraulics, and other physical problems).
  5. To provide necessary background in this area for possible advanced studies in many fields.

COURSE OUTLINE:

  1. Complex Numbers
  2. Analytic Functions
  3. Elementary Function of a Complex Variable
  4. Mappings of Elementary Functions
  5. Complex Integration
  6. Power Series
  7. Residues and Poles (Calculus of Residues)

Revised 6/08