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Department of Mathematical Sciences, Unit Catalogue 2009/10


MA50190: Advanced mathematical methods

Click here for further information Credits: 6
Click here for further information Level: Masters
Click here for further information Period: Semester 1
Click here for further information Assessment: EX 100%
Click here for further informationSupplementary Assessment: MA50190 Mandatory extra work (where allowed by programme regulations)
Click here for further information Requisites:
Description: Aims:
To study advanced mathematical methods and techniques relevant to solving problems which arise in applications modelled by differential equations (both ordinary and partial) and integral equations. To provide a firm basis of useful techniques for many subsequent courses in applied mathematics.
Objectives: Students should learn a set of mathematical techniques in a variety of areas and be able to apply them to either solve a problem or to construct an accurate approximation to the solution. They should demonstrate an understanding of both the theory and the range of applications (including the limitations) of all the techniques studied.

Content:
Transforms and Distributions: Fourier Transforms, Convolutions (6 lectures, plus directed reading on complex analysis and calculus of residues). Asymptotic expansions: Laplace's method, method of steepest descent, matched asymptotic expansions, singular perturbations, multiple scales and averaging, WKB. (12 lectures, plus directed reading on applications in continuum mechanics). Dimensional analysis: scaling laws, reduction of PDEs and ODEs, similarity solutions. (6 lectures, plus directed reading on symmetry group methods). References: L. Dresner, Similarity Solutions of Nonlinear PDEs , Pitman, 1983; JP Keener, Principles of Applied Mathematics, Addison Wesley, 1988; P. Olver, Symmetry Methods for PDEs, Springer; E.J. Hinch, Perturbation Methods, CUP.
NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.