MAU23204 Introduction to complex analysis

Module Code	MAU23204
Module Title	Introduction to complex analysis
Semester taught	Semester 2
ECTS Credits	5
Module Lecturer
Module Prerequisites	MAU11204 Analysis on the real line OR MAU23203 Analysis in several real variables

This module is examined in a 2-hour examination at the end of Semester 2.
Students are assessed based on the exam alone.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

11 weeks of teaching with 3 lectures per week.

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

Apply basic theorems on complex sequences and series, with a special emphasis on power series.
Use these theorems to calculate coefficients and radii of convergence of power series.
State basic properties of analytic functions and apply known theorems to simple examples.
State Cauchy's theorems and use them to compute contour integrals.
Prove and use properties of important examples of analytic functions, including rational, exponential, logarithmic, trigonometric and hyperbolic functions.