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.
