Associate Professor of Mathematics
Rose-Hulman Institute of Technology

MA 367 Functions of a Complex Variable
From the catalog
Prerequisites: MA 113
Course Description: Elementary properties of analytic functions including Cauchy's theorem and its consequences, Laurent series, the Residue Theorem, and mapping properties of analytic functions.
This is a course on the calculus of functions of a complex variable and how it differs from functions of real variables. The course will emphasize a geometrical approach and an applications based approach, with some of the theoretical and analytical background for those who have had more advanced courses, than MA 113.

Functions of complex variables have a variety of applications and have been studied for centuries from their use in providing the correct framework for solving ordinary differential equations and partial differential equations. They are also used for generating dynamics and fractals, and the geometric structure of Riemann surfaces. The figure depicts the Riemann surface generated by the square root of z
Text Book:
Visual Complex Analysis by Tristan Needham

Click on Picture to GoTo Oxford University Press
to find out more about the text.
Topics:
  • Geometry and Complex Arithmetic
  • Complex Functions as Transformations
  • Mobius Transformations and Inversions
  • Differentiation
  • Geometry of Differentiation
  • Non-Euclidean Geometry
  • Winding Numbers and Topology
  • Complex Integration
  • Cauchy's Theorem and Formula
  • Applications
Evaluation will be by
homework(50%), quizzes (25%), final exam (25%) and class participation (+/- 5%).