MATH365-12S2 (C) Semester Two 2012
Applications of Complex Variables

Description

Complex variables with applications and special functions are essential tools for pure and applied mathematicians, scientists and engineers.
The material covered is a mix beautiful theory (e.g. Taylors theorem for functions of a complex variable),  applications and computational techniques (e.g. calculation of Laplace transforms via contour integration).

Learning Outcomes

• At the end of the course the student will be familiar with the following topics:
 - complex numbers and functions of a complex variable
 - analytic functions and the Cauchy-Riemann equations
 - cauchy's theorem.  Taylor and Laurent series.  Singularities

• Students will be able to evaluate definite integrals and  calculate Laplace transforms using the calculus of residues

• Students will also be familiar with:
 - conformal mappings and applications to electrostatics, heat and fluid flow
 - legendre polynomials, properties of these, and applications to sphere in a  uniform electric field, potential of a ring of charge

Alternatively students will be familiar with the properties and applications of another family of special functions.

Pre-requisites

Restrictions

For further information see Mathematics and Statistics.