Green's Functions with Applications

ISBN: 9781482251029 出版年：2015 页码：673 Duffy, Dean G CRC Press

Acknowledgments Author Preface List of Definitions Historical Development Mr. Green's Essay Potential Equation Heat Equation Helmholtz's Equation Wave Equation Ordinary Differential Equations Background Material Fourier Transform Laplace Transform Bessel Functions Legendre Polynomials The Dirac Delta Function Green's Formulas What Is a Green's Function? Green's Functions for Ordinary Differential Equations Initial-Value Problems The Superposition Integral Regular Boundary-Value Problems Eigenfunction Expansion for Regular Boundary-Value Problems Singular Boundary-Value Problems Maxwell's Reciprocity Generalized Green's Function Integro-Differential Equations Green's Functions for the Wave Equation One-Dimensional Wave Equation in an Unlimited Domain One-Dimensional Wave Equation on the Interval 0 < x < L Axisymmetric Vibrations of a Circular Membrane Two-Dimensional Wave Equation in an Unlimited Domain Three-Dimensional Wave Equation in an Unlimited Domain Asymmetric Vibrations of a Circular Membrane Thermal Waves Diffraction of a Cylindrical Pulse by a Half-Plane Leaky Modes Water Waves Green's Functions for the Heat Equation Heat Equation over Infinite or Semi-Infinite Domains Heat Equation within a Finite Cartesian Domain Heat Equation within a Cylinder Heat Equation within a Sphere Product Solution Absolute and Convective Instability Green's Functions for the Helmholtz Equation Free-Space Green's Functions for Helmholtz's and Poisson's Equation Method of Images Two-Dimensional Poisson's Equation over Rectangular and Circular Domains Two-Dimensional Helmholtz Equation over Rectangular and Circular Domains Poisson's and Helmholtz's Equations on a Rectangular Strip Three-Dimensional Problems in a Half-Space Three-Dimensional Poisson's Equation in a Cylindrical Domain Poisson's Equation for a Spherical Domain Improving the Convergence Rate of Green's Functions Mixed Boundary Value Problems Numerical Methods Discrete Wavenumber Representation Laplace Transform Method Finite Difference Method Hybrid Method Galerkin Method Evaluation of the Superposition Integral Mixed Boundary Value Problems Appendix: Relationship between Solutions of Helmholtz's and Laplace's Equations in Cylindrical and Spherical Coordinates Answers to Some of the Problems Author Index Subject Index