MA321 (Calculus and Mathematical Modelling), MA322 (Proofs and Numbers), MA323 (Matrices and Probability) at Stage 1 and MA552 (Analysis), MA553 (Linear Algebra), MA588 (Mathematical Techniques and Differential Equations) at Stage 2, or students must have studied material equivalent to that covered in these modules.
OverviewThe lectures will introduce students to asymptotic and perturbation methods for the approximate evaluation of integrals and to obtain approximations for solutions of ordinary differential equations. These methods are widely used in the study of physically significant differential equations which arise in Applied Mathematics, Physics and Engineering. The material is chosen so as to demonstrate a range of mathematical techniques available and to illustrate some different applications which are amenable to such analysis.
This module appears in:
42-48 lectures and example classes
Method of assessment
80% Examination, 20% Coursework
14. Indicative Reading List
C M Bender and S A Orszag, "Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory", Springer-Verlag, New York (1999)
J D Murray, Asymptotic Analysis, Springer-Verlag, New York (1997)
All books are available in the Templeman Library.
On successful completion of this module, students will:
a) have developed a familiarity with the use of asymptotic techniques in the study of integrals and differential equations;
b) be able to obtain asymptotic approximations of various types of integrals;
c) be able to determine approximate solutions of linear differential equations;
d) be able to generate matched asymptotic expansions for singular perturbation and boundary layer problems
e) be able to use WKB (Wentzel-Kramers-Brillouin), multiple scales and related methods to obtain asymptotic expansions of solutions of some differential equations