Perturbation Methods in Engineering

  • Introduction

  • Order Relations

  • Gauge Functions

  • Non-dimensionalizing Equations

  • Regular Perturbation- Von Karman's Eq.

  • Regular Perturbation- Heat Transfer Problem

  • Regular Perturbation- Method of Ansatz

  • Regular Perturbation- Laplace's Eq.

  • Regular Perturbation- Flow Past Cylinder

  • Singular Perturbation- Nonlinear Spring

  • Strained Coordinates- Lindstedt

  • Strained Coordinates- PLK

  • Strained Coordinates- Pritulo

  • Boundary Layer Theory- Prandtl

  • Inner Approximation- Erdelyi

  • Van Dyke's Matching Principle

  • Multiple Scales

  • Nonlinear Scales

  • The GST Method

  • The WKB Method 

Advanced Perturbation Methods

  • WKB Method (Type I and Type II) with Multiple Distinguished Limits

  • Latta's Method of Composite Expansions

  • Method of Averaging (van der Pol's Mehtod/ Krylov- Bogoliubov Method

  • Asymptotic Expansion of Integrals (Watson's Lemma)

  • Laplace's Method