Applied Mathematics 5480

Methods of Applied Mathematics 4: Approximation Methods

Spring 2011

Instructor: Office / Office hours:	Keith Julien ECOT 321 / MWF 11-12.
Class hours/location: Text:	MWF 10.00-10.50 am / ECCR 108 Perturbation Methods (Hinch; Cambridge Text in Applied Mathematics 1991) Advanced Mathematical Methods for Scientists and Engineers Asymptotic Methods and Perturbation Theory (Bender & Orszag; Springer)
Homework policies:	There will be 6-7 assignments (approximately bi-weekly) Collaboration to get ideas and insights is encouraged - copying is not permitted. Use of Mathematica (or Maple) for simplifying tedious steps is encouraged (as long as it is clear how a hand-based solution could have been carried out).
Final Project:	Download class projects (tarfile)
Final Grade:	Homeworks (60%) + Project (40%)
Homeworks:	TBA
Resources: Mathematica Notebooks	Regular perturbation; polynomial roots Padé convergence acceleration for a Stieltjes function Conversion from Taylor- to continued fraction expansion Laplace integral - integration by parts Laplace's method - higher order terms Laplace integrals - Watson's lemma Gamma function expansion using steepest descent Fourier-Laplace method to get ODE solution in integral form ODE expansion around regular point ODE expansion around irregular singular point Perturbation expansions for the projectile problem: --- By plugging in an assumed series and equating coefficients --- By parametric differentiation and by iteration First example on boundary layers Second example on boundary layers Numerical solution of boundary value problems