Perturbation Methods in Science and Engineering

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

Autorentext

Reza N. Jazar is a Professor of Mechanical Engineering. Reza received his PhD degree from Sharif University of Technology, Tehran, Iran; MSc and BSc from Tehran Polytechnic, Tehran, Iran. His areas of expertise include Nonlinear Dynamic Systems and Applied Mathematics. He obtained original results in non-smooth dynamic systems, applied nonlinear vibrating problems, time optimal control robotics, and mathematical modeling of vehicle dynamics and stability. He authored several monographs in vehicle dynamics, robotics, dynamics, vibrations, mathematics, and published numerous professional articles, as well as book chapters in research volumes. Most of his textbooks have been adopted by many universities for teaching and research and by many research agencies as standard model for research results.

Dr. Jazar had the pleasure to work in several Canadian, American, Asian, and Middle Eastern universities, as well as several years in Automotive Industries all around the world. Working in different engineering firms and educational systems provide him a vast experience and knowledge to publish his researches on important topics in engineering and science. His unique style of writing helps readers to learn the topics deeply in an easy way.

Klappentext

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.

Inhalt
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.