Introduction
Power Series Method
Introduction
Algebraic Method (Method of Undetermined Coefficients)
Solution at Ordinary Point of an Ordinary Differential Equation
Solution at a Singular Point (Regular) of an Ordinary
Differential Equation
Remarks on the Frobenius Solution at Irregular Singular Points
Taylor Series Method
Asymptotic Method
Introduction
Asymptotic Solutions at Irregular Singular Points at Infinity
Asymptotic Solutions of Perturbed Problems
Solutions to ODEs Containing a Large Parameter
Perturbation Techniques
Introduction
Regular Perturbation Theory
Singular Perturbation Theory
Method of Multiple Scales
Introduction
Method of Multiple Scales
WKB Theory
Introduction
WKB Approximation for Unperturbed Problems
WKB Approximation for Perturbed Problems
Nonperturbation Methods
Introduction
Lyapunov’s Artificial Small-Parameter Method
Delta Expansion Method
Adomian Decomposition Method
Homotopy Methods
Introduction
Homotopy Analysis Method
Homotopy Perturbation Method
Optimal Homotopy Analysis Method
Exercise Problems, Applications, and a Bibliography appear at the end of each chapter.