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.
· 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.
Advanced Undergraduate and Graduate Students in Science and Engineering.