Introduction to Perturbation Techniques

Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises. Algebraic Equations.

Integrals.

The Duffing Equation.

The Linear Damped Oscillator.

Self-Excited Oscillators.

Systems with Quadratic and Cubic Nonlinearities.

General Weakly Nonlinear Systems.

Forced Oscillations of the Duffing Equation.

Multifrequency Excitations.

The Mathieu Equation.

Boundary-Layer Problems.

Linear Equations with Variable Coefficients.

Differential Equations with a Large Parameter.

Solvability Conditions.

Appendices.

Bibliography.

Index.