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Courses / Modules / MATH3088 Complex Analysis

Complex Analysis

When you'll study it
Semester 2
CATS points
ECTS points
Level 6
Module lead
Bernhard Koeck
Academic year

Module overview

Complex Analysis is the theory of functions in a complex variable. While the initial theory is very similar to Analysis (i.e, the theory of functions in one real variable as seen in the second year), the main theorems provide a surprisingly elegant, foundational and important insight into Analysis and have far-reaching and enlightening applications to functions in real variables.

After introducing differentiability of complex functions and contour integrals, the highlights of this module are presented: Cauchy’s Theorem, Cauchy’s Integral Formula and the Residue Theorem. Finally, the theory is applied to prove the Fundamental Theorem of Algebra, to evaluate real integrals, to provide partial-fraction and infinite-product expansions of classical functions and to introduce and study the Gamma function (a fundamental function that for example affords an asymptotic formula for factorials and a computation of the integral of the Gaussian bell curve).

One of the pre-requisites for MATH6094

Linked modules

Pre-requisites: MATH1048 AND MATH2039