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Full Description
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.
Contents
Chapter 1 Introduction
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
