On successful completion of this module, students will be able to:

Use basic theorems on complex sequences and series, with a particular
emphasis on power series. Calculate coefficients and radii of convergence
of power series using these theorems.

Demonstrate a familiarity with the basic properties of analytic
functions. Apply these theorems to simple examples.

State correctly the theorems of Cauchy and Morera.
Calculate, using Cauchy's theorem and its corollaries, the
values of contour integrals.

Prove and apply properties of important examples of analytic
functions, including rational functions, the exponentential and
logarithmic functions, trigonometric and hyperbolic functions
and elliptic functions.

Module Content

Aims to introduce complex variable theory and reach the residue theorem, applications of that to integral evaluation.

Power series

Analytic functions

Complex Integration

Residue calculus

Elliptic functions

Assessment Detail

This module will be examined in a 2 hour examination in Trinity term.