Credits:
 6 
Level:
 Honours (FHEQ level 6) 
Period: 
Semester 2

Assessment:
 EX 100% 
Supplementary Assessment:  MA30056 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:
 Before taking this unit you must take MA20218 and take MA20219 
Description:
 Aims & Learning Objectives: Aims: The aim of this course is to cover the standard introductory material in the theory of functions of a complex variable and to cover complex function theory up to Cauchy's Residue Theorem and its applications.
Objectives:
Students should end up familiar with the theory of functions of a complex variable and be capable of calculating and justifying power series, Laurent series, contour integrals and applying them.
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. Pathconnectedness. Analyticity and the CauchyRiemann equations. Harmonic functions. Cauchy's theorem. Cauchy's Integral Formulae 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.

Programme availability:

MA30056 is Optional on the following programmes:
Department of Computer Science
 USCMAFB01 : BSc Computing (Fulltime)  Year 3
 USCMAKB01 : BSc Computing (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAFB13 : BSc (hons) Computer Science with Mathematics (Fulltime)  Year 3
 USCMAKB14 : BSc (hons) Computer Science with Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USCMAAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
Department of Mathematical Sciences
 USMAAFB15 : BSc (hons) Mathematical Sciences (Fulltime)  Year 3
 USMAAKB16 : BSc (hons) Mathematical Sciences (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB13 : BSc (hons) Mathematics (Fulltime)  Year 3
 USMAAKB14 : BSc (hons) Mathematics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAFB01 : BSc (hons) Mathematics and Statistics (Fulltime)  Year 3
 USMAAKB02 : BSc (hons) Mathematics and Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAAB14 : BSc (hons) Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFB05 : BSc (hons) Statistics (Fulltime)  Year 3
 USMAAKB06 : BSc (hons) Statistics (Fulltime with Thick Sandwich Placement)  Year 4
 USMAAAB06 : BSc (hons) Statistics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 3
 USMAAFM14 : MMath Mathematics (Fulltime)  Year 4
 USMAAAM15 : MMath Mathematics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 TSMAAFM09 : MSc Mathematical Sciences (Fulltime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 1
 TSMAAPM09 : MSc Mathematical Sciences (Parttime)  Year 2
Department of Physics
 USXXAFB03 : BSc (hons) Mathematics and Physics (Fulltime)  Year 3
 USXXAKB04 : BSc (hons) Mathematics and Physics with Placement (Fulltime with Thick Sandwich Placement)  Year 4
 USXXAAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Fulltime with Study Year Abroad)  Year 4
 USXXAFM01 : MSci (hons) Mathematics and Physics (Fulltime)  Year 3
