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Module MA23204: Introduction to Complex Analysis
- Credit weighting (ECTS)
-
5 credits
- Semester/term taught
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Hilary term 2019-20
- Contact Hours
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11 weeks, 3 lectures per week
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- Lecturer
- 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.
