
Fourier Methods in Science and Engineering
Description
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Beginning with an overview of the conventional Fourier series theory, this book introduces the generalized Fourier series (GFS), emphasizing its notable rate of convergence when compared to the conventional Fourier series expansions. After systematically presenting the GFS as a powerful and unified solution method for ordinary differential equations and partial differential equations, this book expands on some representative boundary value problems, diving into their multiscale characteristics.
This book will provide readers with the comprehensive foundation necessary for solving a wide spectrum of mathematical problems key to practical applications. It will also be of interest to researchers, engineers, and college students in various science, engineering, and mathematics fields.
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Persons
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.
Content
Chapter 2 Fourier Series Expansions of Functions
Chapter 3 The Generalized Fourier Series with Accelerated Convergence
Chapter 4 The Generalized Fourier Series Solutions of the Euler-Bernoulli Beam Equation.
Chapter 5 Fourier Series for the Derivatives of One-Dimensional Functions
Chapter 6 Fourier Series for the Partial Derivatives of Two-Dimensional Functions
Chapter 7 The Generalized Fourier Series of Functions
Chapter 8 The Generalized Fourier Series of Two-Dimensional Functions
Chapter 9 Multiscale Fourier Series Methods for Linear Differential Equations
Chapter 10 Multiscale Fourier Series Method for the Convection-Diffusion-Reaction Equation
Chapter 11 Bending of Thick Plates on Elastic Foundations
Chapter 12 Wave Propagation in Elastic Waveguides
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