MA PH 451 Mathematical Methods of Physics (This page is under
construction and will be updated, particularly in late November and in
December 2015)
Course objective
To learn advanced mathematical
techniques in physics and practice their application using examples
primarily from quantum and classical mechanics.
Instructor
Andrzej Czarnecki
Office hours: TBA
Topics (tentative)
Approximate solutions of linear ODE:
Singular points of ODE, series expansions, Frobenius series, asymptotic series.
Approximate analysis of nonlinear ODE:
phase space, critical points, separatrices etc.
Approximate evaluation of integrals:
Methods of stationary phase and Laplace.
Perturbation analysis and WKB theory:
Perturbation expansion, asymptotic matching, WKB and boundary layer technique.
Green's function method:
Definition, Green's functions of main differential operators, application to perturbation theory.
Uniform perturbation theory:
Multi scale analysis, method of averaging.
Textbooks
Required textbook
C. Bender and S. Orszag: Advanced Mathematical Methods for Scientists and Engineers, 1999, QA 371 B454.
Additional textbooks
G. Arfken and H. Weber: Mathematical Methods for Physicists
A.H. Nayfeh: Perturbation Methods
R. Courant and D. Hilbert: Methods of Mathematical Physics
E. T. Whittaker and G. N. Watson: A course of modern analysis
F. W. Byron and R. W. Fuller, Mathematics of Classical and Quantum Physics
Last modified: Fri Oct 2 21:33:34 MDT 2015