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MA50186: Complex analysis

Follow this link for further information on academic years Academic Year: 2015/6
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 2
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 25%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment: MA50186 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions Description: Aims & Learning Objectives:
The aim of this course is to develop the theory of functions of a complex variable and to cover complex function theory up to Cauchy's Residue Theorem and its applications. On completion of the course, students should have mastered the essentials of the theory of functions of a complex variable. They should be capable of justifying, and have mastered the calculation of, power series, Laurent series, contour integrals and, through assessed coursework, their application. They should be able to demonstrate an in-depth understanding of the subject.

Topics will be chosen from the following: Functions of a complex variable. Continuity. Complex series and power series. Circle of convergence. The complex plane. Regions, paths, simple and closed paths. Path-connectedness. Analyticity and the Cauchy-Riemann equations. Harmonic functions. Cauchy's theorem. Cauchy's Integral Formula and its application to power series. Isolated zeros. Differentiability of an analytic function. Liouville's Theorem. Zeros, poles and essential singularities. Laurent expansions. Cauchy's Residue Theorem and contour integration. Applications to real definite integrals.
Further information on programme availabilityProgramme availability:

MA50186 is Optional on the following programmes:

Department of Mathematical Sciences
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.