Series and variational methods
4 points * Second semester * Clayton * Prerequisites: MAT2010, MAA2011 and MAA2032
Objectives On the completion of this subject students will be able to recognise ordinary and singular points of linear ordinary differential equations, and apply power series, Frobenius or dominant balance methods as appropriate about these points; extremise integrals via the Euler-Lagrange equations and their extensions; formulate and solve simple isoperimetric problems; understand and use the Rayleigh-Ritz method for solving differential equations.
Synopsis Basic power series methods for ordinary differential equations. Frobenius solutions. Special functions. Asymptotic series. Asymptotic solutions of ordinary differential equations. Sturm-Liouville equations. Euler-Lagrange equations and extensions. End conditions and transversality. Isoperimetric problem. Lagrangian and Hamiltonian dynamics. Applications. Use of direct methods in solving differential equations.
Assessment Examinations (1.5 hours): 85% * Assignments: 15%
Recommended texts
Bender C M and Orszag S A Advanced mathematical methods for scientists and engineers McGraw-Hill, 1978
| Published by Monash University, Clayton, Victoria
3168 Copyright © Monash University 1996 - All Rights Reserved - Caution Authorised by the Academic Registrar December 1996 |