Part1. Preliminaries -- Chapter1. P1: Principles of Perturbations -- Chapter2. P2: Differential Equations -- Chapter3. P3: Approximation of Functions -- Part2. Perturbation Methods -- Chapter4. Harmonic Balance Method -- Chapter5. Straightforward Method -- Chapter6. Lindstedt-Poincaré Method -- Chapter7. Mathieu Equation -- Chapter8. Averaging Method -- Chapter9. Multiple Scales Method.

Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems. Illustrates all key concepts with solved examples; Includes numerous exercises for each chapter; Covers both time and steady state responses of nonlinear differential equations; Covers necessary theory and applied to a variety of topics in optimization and control.