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Module MA23204: Introduction to Complex Analysis

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2019-20
Contact Hours
11 weeks, 3 lectures per week
 Prof. Marius de Leeuw
Learning Outcomes
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.
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
Module Prerequisite
MAU11204, MAU23203
Assessment Detail
This module will be examined in a 2-hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session, with the examination counting for the remaining 85%. Re-assessments if required will consist of 100% exam.