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Module MA2328: Complex Analysis I

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2015-16
Contact Hours
11 weeks, 3 lectures per week
Lecturer
Prof. Dmitri Zaitsev
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 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
Module Prerequisite
Analysis on the Real Line II (MA1124)
or Analysis in Several Real Variables (MA2321)
Assessment Detail
This module will be examined in a 2 hour examination in Trinity term.