Student building 105 room 101 4pm - 6pm on Wednesdays
Advanced mathematical methods for scientists and engineers by Carl M. Bender and Steven Orszag
Introduction
Approximate methods for LDEs
Classification of of singular points
Series expansion near a regular singular point
Behavior near finite irregular singular points
Irregular singular points at infinity and the asymptotic power series
Asymptotic relations
Asymptotic series
Boundary layer theory
Inner, outer and intermediate regions of a boundary
Boundaries of width greater than epsilon and higher order boundary layer theory
Internal boundary layers
Boundary layer theory applied to NLDE
WKB theory
The WKB expansion
Turning points
Tunneling
Inhomogeneous equations
Asymptotic analysis of integrals
Intro
Laplace integrals
Stationary phase approximation
The method of steepest decent
problem set 1 - ordinary and regular singular points, perturbation theory
problem set 2- expansion near singularities in LDEs
Problem set 3 - Boundary layer theory
Tutorial 1
Video, Blackboard 18/3/2020
Video, Blackboard 25/3/2020
Video, Blackboard 22/4/2020
Video, Blackboard 06/5/2020
Video, Blackboard 13/5/2020
Video, Blackboard 20/5/2020
Video, Blackboard 27/5/2020
Video, Blackboard 3/6/2020
Video, Blackboard 10/6/2020
Video, Blackboard 17/6/2020