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.
Author(s): Reza N. Jazar
Publisher: Springer
Year: 2021
Language: English
Pages: 595
City: Cham
Preface
Contents
About the Author
I Preliminaries
1 P1: Principles of Perturbations
1.1 Gauge Function and Order Symbol
1.1.1 The Order Symbol O
1.1.2 The Order Symbol o
1.2 Applied Perturbation Principle
1.2.1 Regular Perturbations
1.2.2 Singular Perturbations
1.3 Applied Weighted Residual Methods
1.4 Chapter Summary
1.5 Key Symbols
2 P2: Differential Equations
2.1 Applied Differential Equations
2.1.1 Phase Plane
2.1.2 Limit Cycle
2.1.3 State Space
2.1.4 State-Time Space
2.2 Chapter Summary
2.3 Key Symbols
3 P3: Approximation of Functions
3.1 Applied Power Series Expansion
3.2 Applied Fourier Series Expansion
3.3 Applied Orthogonal Functions
3.4 Applied Elliptic Functions
3.5 Chapter Summary
3.6 Key Symbols
II Perturbation Methods
4 Harmonic Balance Method
4.1 First Harmonic Balance
4.2 Higher Harmonic Balance
4.3 Energy Balance Method
4.4 Multi-degrees-of-Freedom Harmonic Balance
4.5 Chapter Summary
4.6 Key Symbols
5 Straightforward Method
5.1 Chapter Summary
5.2 Key Symbols
6 Lindstedt-Poincaré Method
6.1 Periodic Solution of Differential Equations
6.2 Chapter Summary
6.3 Key Symbols
7 Mathieu Equation
7.1 Periodic Solutions of Order n=1
7.2 Periodic Solutions of Order nN
7.3 Mathieu Functions
7.4 Chapter Summary
7.5 Key Symbols
8 Averaging Method
8.1 Chapter Summary
8.2 Key Symbols
9 Multiple Scale Method
9.1 Chapter Summary
9.2 Key Symbols
A Ordinary Differential Equations
B Trigonometric Formulas
C Integrals of Trigonometric Functions
D Expansions and Factors
E Unit Conversions
Index
