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Department of Mathematical Sciences, Unit Catalogue 2011/12


MA50186: Complex analysis

Click here for further information Credits: 6
Click here for further information Level: Masters UG & PG (FHEQ level 7)
Click here for further information Period: Semester 2
Click here for further information Assessment: CW 25%, EX 75%
Click here for further information Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Click here for further information Requisites:
Click here for further information 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.

Content:
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.
Click here for further informationProgramme availability:

MA50186 is Optional on the following programmes:

Department of Mathematical Sciences
NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.