Perturbations

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