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E-raamat: Fourier Methods in Science and Engineering [Taylor & Francis e-raamat]

(Advanced Information Services (AIS), China), (JIANGHAN UNIVERSITY, CHINA)
  • Formaat: 324 pages, 41 Tables, black and white; 59 Line drawings, black and white; 59 Illustrations, black and white
  • Ilmumisaeg: 21-Nov-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003194859
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  • Taylor & Francis e-raamat
  • Hind: 138,48 €*
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Fourier Methods in Science and EngineeringSuurem pilt
  • Formaat: 324 pages, 41 Tables, black and white; 59 Line drawings, black and white; 59 Illustrations, black and white
  • Ilmumisaeg: 21-Nov-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9781003194859
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003194859
This innovative textbook applies the Modified Fourier Series to a variety of problems commonly encountered within science and engineering, equipping the reader with a clear pathway through which to use the Fourier method as a solution technique for a wide range of differential equations and boundary value problems. Beginning with an overview of the conventional Fourier series theory, the book goes on to introduce the modified Fourier series (MFS), emphasising its notable rate of convergence when compared to traditional Fourier series expansions. It particularly focuses on acoustics, elasticity, structural vibrations and coupled vibro-acoustics. Systematically presenting MFS as a powerful and unified solution method for ordinary differential equations, partial differential equations and boundary value problems, the book goes on to expand on boundary value problems, diving into hot topics such as multi-domain, multi- physics, and multi-scale characteristics. It will include exemplary MATLAB code to aid students in practically applying MFS. The book will provide students with a comprehensive foundation necessary when solving a wide range of mathematical problems key to engineering applications. It will be of interest to Mechanical engineering and engineering mathematics students.

This innovative textbook applies the Modified Fourier Series to a variety of problems commonly encountered within science and engineering, equipping the reader with a clear pathway through which to use the Fourier method as a solution technique for a wide range of differential equations and boundary value problems.

Preface xi
Acknowledgments xiii
Authors xv
Chapter 1 Introduction
1(10)
1.1 Scales and Scale Effects
1(1)
1.2 Multiscale Phenomena and Multiscale Analysis Methods
2(4)
1.3 Fourier Series Methods in Scientific and Engineering Applications
6(1)
1.4 Scope of this Book
7(4)
References
8(3)
Chapter 2 Fourier Series Expansions of Functions
11(20)
2.1 Periodic Functions and their Fourier Series Expansions
11(6)
2.2 Convergence of Fourier Series Expansions
17(4)
2.3 Fourier Series for the Derivatives of Functions
21(10)
References
30(1)
Chapter 3 The Generalized Fourier Series with Accelerated Convergence
31(30)
3.1 Improving the Convergence of Fourier Series
31(10)
3.2 The Generalized Fourier Cosine Series Expansion with Accelerated Convergence
41(10)
3.3 The Generalized Fourier Sine Series with Accelerated Convergence
51(5)
3.4 The Generalized Fourier Series Expansion with Accelerated Convergence
56(5)
References
60(1)
Chapter 4 The Generalized Fourier Series Solutions of the Euler-Bernoulli Beam Equation
61(28)
4.1 Linear Differential Equations with Constant Coefficients
61(3)
4.2 Characteristic Solutions of the Beam Equation
64(3)
4.3 Fourier Series Solutions of the Beam Problems
67(3)
4.4 The Generalized Fourier Series Solutions
70(8)
4.5 Convergence Assessment
78(1)
4.6 Numerical Examples
79(10)
References
87(2)
Chapter 5 Fourier Series for the Derivatives of One-Dimensional Functions
89(16)
5.1 Integral Formulas Regarding the Derivatives of Functions
89(2)
5.2 Fourier Coefficients for the Derivatives of Functions
91(4)
5.3 Examples
95(8)
5.4 Sufficient Conditions for the Term-by-Term Differentiations of Fourier Series
103(2)
Chapter 6 Fourier Series for the Partial Derivatives of Two-Dimensional Functions
105(38)
6.1 Integral Formulas Regarding Higher Order Partial Derivatives of Two-Dimensional Functions
105(3)
6.2 Fourier Coefficients for Partial Derivatives of Two-Dimensional Functions
108(21)
6.2.1 The Full-Range Fourier Series for the Partial Derivatives
108(16)
6.2.2 The Half-Range Fourier Series for the Partial Derivatives
124(5)
6.3 Examples
129(1)
6.4 Sufficient Conditions for Term-by-Term Differentiations of the Fourier Series of Two-Dimensional Functions
130(13)
Appendix: Additional Integral Formulas
135(8)
Chapter 7 The Generalized Fourier Series of Functions
143(16)
7.1 Structural Decompositions of One-Dimensional Functions
143(1)
7.2 Generalized Fourier Series of One-Dimensional Functions
144(8)
7.2.1 The Generalized Full-Range Fourier Series of One-Dimensional Functions
144(4)
7.2.2 The Generalized Half-Range Fourier Cosine Series of One-Dimensional Functions
148(2)
7.2.3 The Generalized Half-Range Fourier Sine Series of One-Dimensional Functions
150(2)
7.3 The Polynomial-Based Generalized Fourier Series for One-Dimensional Functions
152(1)
7.4 Examples
153(6)
7.4.1 Error Indexes of the Series Approximations
153(1)
7.4.2 Convergence Characteristics
154(2)
7.4.3 Reproducing Property of Polynomials
156(1)
7.4.4 Approximation Accuracy
156(3)
Chapter 8 The Generalized Fourier Series of Two-Dimensional Functions
159(26)
8.1 Structural Decompositions of Two-Dimensional Functions
159(4)
8.2 The Generalized Fourier Series Expansions for Two-Dimensional Functions
163(13)
8.2.1 The Generalized Full-Range Fourier Series
163(7)
8.2.2 The Generalized Half-Range Fourier Sine-Sine Series
170(6)
8.3 The Polynomial-Based Generalized Fourier Series Expansions
176(1)
8.4 Numerical Characteristics of the Generalized Fourier Series
177(8)
8.4.1 Error Norms of Simultaneous Series Approximations
178(1)
8.4.2 Convergence Characteristics
179(2)
8.4.3 The Accuracy of the Generalized Fourier Series
181(4)
Chapter 9 Multiscale Fourier Series Methods for Linear Differential Equations
185(26)
9.1 The Generalized Fourier Series Solutions of One-Dimensional Boundary Value Problems
185(4)
9.1.1 The Generalized Full-Range Fourier Series Solutions
185(2)
9.1.2 The Generalized Half-Range Fourier Cosine Series Solutions
187(1)
9.1.3 The Generalized Half-Range Fourier Sine Series Solutions
188(1)
9.2 The Generalized Fourier Series Solutions for Two-Dimensional Boundary Value Problems
189(5)
9.2.1 The Generalized Full-Range Fourier Series Solutions
189(3)
9.2.2 The Generalized Half-Range Fourier Sine-Sine Series Solutions
192(2)
9.3 Limitations of the Polynomial-Based Generalized Fourier Series Methods
194(2)
9.4 Determination of the General Solution
196(8)
9.4.1 The General Solutions of One-Dimensional Boundary Value Problems
196(1)
9.4.2 The General Solutions of Two-Dimensional Boundary Value Problems
197(7)
9.5 Equivalent Transformation of the Solution
204(2)
9.6 Introduction of the Supplementary Solution
206(1)
9.7 The Multiscale Characteristic of the Solution
207(1)
9.8 Solution Schemes
208(3)
Chapter 10 Multiscale Fourier Series Method for the Convection-Diffusion-Reaction Equation
211(42)
10.1 Multiscale Fourier Series Solution for One-Dimensional Convection-Diffusion-Reaction Equation
212(8)
10.1.1 Description of the Problem
212(1)
10.1.2 The General Solution
212(2)
10.1.3 The Supplementary Solution
214(2)
10.1.4 The Particular Solution
216(3)
10.1.5 The Multiscale Fourier Series Solution
219(1)
10.2 One-Di mensional Numerical Examples
220(13)
10.2.1 Convergence Characteristics
221(6)
10.2.2 Computational Efficiency
227(2)
10.2.3 Multiscale Characteristics
229(4)
10.3 Multiscale Fourier Series Solution for Two-Dimensional Convection-Diffusion-Reaction Equation
233(8)
10.3.1 Description of the Problem
234(1)
10.3.2 The General Solution
234(2)
10.3.3 The Supplementary Solution
236(2)
10.3.4 The Particular Solution
238(3)
10.3.5 The Multiscale Fourier Series Solution
241(1)
10.4 Two-Dimensional Numerical Examples
241(12)
10.4.1 Convergence Characteristics
243(4)
10.4.2 Multiscale Characteristics
247(3)
References
250(3)
Chapter 11 Bending of Thick Plates on Elastic Foundations
253(26)
11.1 Description of the Problem
253(2)
11.2 The Multiscale Fourier Series Solutions
255(9)
11.2.1 The General Solution of the Transverse Displacement
255(2)
11.2.2 The General Solution of the Stress Function
257(1)
11.2.3 Expressions of the Multiscale Fourier Series Solutions
258(2)
11.2.4 Equivalent Transformation of the Solutions
260(2)
11.2.5 Expressions of Stress Resultants
262(2)
11.3 The Solution Obtained from the Energy Principle
264(2)
11.4 Numerical Examples
266(13)
11.4.1 Convergence Characteristics
267(4)
11.4.2 Multiscale Characteristics
271(6)
References
277(2)
Chapter 12 Wave Propagation in Elastic Waveguides
279(44)
12.1 Description of the Problem
279(1)
12.2 The Multiscale Fourier Series Solutions
280(20)
12.2.1 The Differential Equations of Modal Functions
281(1)
12.2.2 Structural Decomposition of Modal Functions
282(1)
12.2.3 Expressions of Boundary Functions Expanded along the y-Direction
282(11)
12.2.4 Expressions of Boundary Functions Expanded along the x-Direction
293(1)
12.2.5 Expressions of Internal and Corner Functions
294(5)
12.2.6 Expressions of the Multiscale Fourier Series Solution
299(1)
12.2.7 Expressions of Stress Resultants
300(1)
12.3 Solving for Solutions
300(2)
12.4 Numerical Examples
302(7)
12.5 Wave Propagations in a Square Waveguide
309(14)
12.5.1 Frequency Spectra
310(1)
12.5.2 Wave Modes
311(10)
References
321(2)
Index 323
Dr. Wen L. Li received his B.S. (1982) in Physics from Liaoning Teachers University in Dalian, China; M.Eng. (1984) in Vehicle Engineering from Beijing Institute of Technology in Beijing, China; and Ph.D. (1991) in Mechanical Engineering from University of Kentucky in Lexington, USA. From 1992 to 1995, he worked with the Case Corporation as Technical Specialist. From 1995 to 2004, he worked with the United Technologies Carrier Corporation as Sr. Staff Engineer and United Technologies Research Center as Principal Engineer. In 2004, he joined the Mississippi State University as an Associate Professor in Mechanical Engineering. In 2007, he moved to Wayne State University as an Associate Professor of Mechanical Engineering. In 2014, Dr. Li started the Advanced Engineering and Technologies company, and in 2016, the Advanced Information Services company in China as the founder and general manager. Dr. Li has author/co-authored about 60 journal papers, 1 book, and 3 book chapters. He is the inventor or co-inventors of more than 30 technical patents. He is the Editor-in-Chief of Open Journal of Acoustics (OJA), member of Editorial Board of several other journals, and co-chair of Prediction and Modeling Technical Committee of Institute of Noise Control Engineering (INCE) and member of Structural Vibration and Acoustics Committee of Acoustical Society of America (ASA). He has chaired/co-chaired dozens of technical sessions of international conferences. His research and experience are mostly related to numerical methods, computer modeling and simulations, dynamics systems, acoustics, and machinery designs.

Dr. Weiming Sun received his B.E. (1995) in Structural Strength of Spacecraft; M.E. (1998) in Solid Mechanics both from National University of Defense Technology in Changsha, China; and Ph.D. (2011) in Solid Mechanics from Beijing Jiaotong University in Beijing, China. Under the supervision of Prof. Zimao Zhang, his doctorate research was focused on proposing a set of general formulas for the Fourier series of higher order (partial) derivatives of one- and two- dimensional functions, developing the generalized Fourier series method for linear differential equations with constant coefficients, and applying it to boundary value problems commonly encountered in engineering applications. After receiving his Ph.D. degree, Dr. Sun became a full-time lecturer in the Department of Mathematics at Jianghan University in Wuhan, China. He has published six journal papers.
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