
Module Availability 
Module Availability:

Semester 2




Assessment Pattern 
Unit(s) of Assessment

Weighting Towards Module Mark( %)

Examination (End of semester)

100%

Qualifying Condition(s)
University general regulations refer.




Module Overview 
The module focuses on several topics in mathematical physics highlighting the importance of linear vector spaces, line and surface integrals and associated theorems, the theory of functions of a complex variables and complex integration methods.




Prerequisites/Corequisites 
PHY2056 – Mathematical, Quantum and Computational Physics.




Module Aims 
To provide a sound grounding in the basic theorems, methods and applications of functions of a complex variable and a range of advanced integration techniques.




Learning Outcomes 
Students will have a solid understanding of and be able to work with derivatives and integrals of vector functions and appreciate their importance in almost every area of applied mathematics. They will be able to make use of vector integral theorems to solve a range of problems.
They willl appreciate the meaning of and be able to test a function for analyticity and also identify and classify poles and other singular points of functions. Students should be familiar with methods for performing real and complex variable integrals by complex contour integration.




Module Content 
Vector Analysis
Revision of vector multiplication and differentiation, vector fields; directional derivative (grad); line and surface integrals; Green’s Theorem in the plane; the divergence and the Divergence (Gauss’s) Theorem; the curl and Stoke’s Theorem; examples. (8 lectures).
Theory of functions of a Complex Variable:
Functions of a complex variable, continuity, differentiability, the CauchyReimann conditions, relationship to Laplace problems in 2¿dimensions, analyticity, singularities, poles; complex integration, Cauchy's theorem; residues and the residue theorem; Taylor and Laurent series; application of residue theorem for evaluation of integrals; examples. (12 lectures).




Methods of Teaching/Learning 
24 hours of lecture classes.




Selected Texts/Journals 
i. M L Boas, Mathematical Methods in the Physical Sciences, Third Edition,Wiley 2006
ii. G Arfken and H B Weber, Mathematical Methods for Physicists, Academic Press, 2005




Last Updated 
August 2010. 
