Cover Image

Green's functions with applications /

Show other versions (3)
Bibliographic Details
Main Author: Duffy, Dean G. (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, [2015]
Edition:Second edition.
Series:Advances in applied mathematics.
Subjects:
Green's functions.
Differential equations.
Fonctions de Green.
Équations différentielles.
Differential equations
Green's functions
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Acknowledgments
  • Author
  • Preface
  • List of Definitions
  • Historical Development
  • Mr. Greens Essay
  • Potential Equation
  • Heat Equation
  • Helmholtzs Equation
  • Wave Equation
  • Ordinary Differential Equations
  • Background Material
  • Fourier Transform
  • Laplace Transform
  • Bessel Functions
  • Legendre Polynomials
  • The Dirac Delta Function
  • Greens Formulas
  • What Is a Greens Function?
  • Greens 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
  • Maxwells Reciprocity
  • Generalized Greens Function
  • Integro-Differential Equations
  • Greens 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
  • Greens 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
  • Greens Functions for the Helmholtz Equation
  • Free-Space Greens Functions for Helmholtzs and Poissons Equation
  • Method of Images
  • Two-Dimensional Poissons Equation over Rectangular and Circular Domains
  • Two-Dimensional Helmholtz Equation over Rectangular and Circular Domains
  • Poissons and Helmholtzs Equations on a Rectangular Strip
  • Three-Dimensional Problems in a Half-Space
  • Three-Dimensional Poissons Equation in a Cylindrical Domain
  • Poissons Equation for a Spherical Domain
  • Improving the Convergence Rate of Greens 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 Helmholtzs and Laplaces Equations in Cylindrical and Spherical Coordinates
  • Answers to Some of the Problems
  • Author Index
  • Subject Index.