Green's Functions
Description
Green's functions represent one of the classical and widely used issues in the area of differential equations.
This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions.
The book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.
Reviews / Votes
"[...] the book is a useful source for everyone who is studying or working in fields of science, finance, or engineering that involve practical solutions of partial differential equations."
L'Enseignement Mathématique
2/2012
"The monograph is a valuable source to any researcher or postgraduate student working in applied sciences or engineering that concern practical solutions of partial or ordinary differential equations."
Marius Ghergu,
Zentralblatt für Mathematik
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Content
Preface
Contents
Chapter 0. Introduction
Chapter 1. Green's Functions for ODE
Chapter 2. The Laplace Equation
Chapter 3. The Static Klein-Gordon Equation
Chapter 4. Higher Order Equations
Chapter 5. Multi-Point-Posed Problems
Chapter 6. PDE Matrices of Green's type
Chapter 7. Diffusion Equation
Chapter 8. Black-Scholes Equation
Appendix. Answers to Chapter Exercises
Bibliography
Index