Complex Analysis module (MA32006)

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Credits

15

Module code

MA32006

About the module

This module introduces the notions of differentiation and integration for functions of a complex variable. It develops the theory with important applications such as evaluation of path integrals via residue calculus, the fundamental theorem of algebra and conformal mappings. This module is mandatory for students taking the BSc or MMath in Mathematics and may optionally be taken in combination with other modules by students on any of the Mathematics combined degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA21001 and MA22001, or equivalents.

Indicative Content

  • Algebraic properties of complex numbers

  • Definition of the derivative; Cauchy-Riemann equations

  • Power series; radius of convergence

  • Logarithmic, exponential and trigonometrical functions; branch points

  • Line integrals. The Cauchy integral theorem and integral formula

  • The Cauchy formula for derivatives; Taylor series

  • Liouville's theorem; fundamental theorem of algebra

  • Laurent's theorem; poles and the residue theorem; zeros of analytic functions

  • Evaluation of integrals

  • Conformal mappings

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).

Credit Rating

This module is a Scottish Higher Education Level 3 or SCQF level 9 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.