Complex Analysis module (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.
Students taking this module must have achieved a pass mark in each of the modules MA21001 and MA22001, or equivalents.
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
Delivery and Assessment
The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).
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.