β Scribed by Reza N. Jazar
No coin nor oath required. For personal study only.
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.
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-PoincarΓ© 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
π SIMILAR VOLUMES
<p>As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustra
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications.Appeals to researchers and graduate students who require tools to investigate stochastic systems.
The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution - for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. In some a
<span>The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mecha