This innovative book discusses and applies the generalized Fourier Series to a variety of problems commonly encountered within science and engineering, equipping the readers with a clear pathway through which to use the Fourier methods 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, 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.
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
Biography
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.
