ABSTRACT

Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary

chapter 1|17 pages

Some Basic Results

chapter 2|29 pages

The Concept of Green’s Functions

chapter 3|37 pages

Sturm-Liouville Systems

chapter 4|37 pages

Bernoulli’s Separation Method

chapter 5|22 pages

Integral Transforms

chapter 6|32 pages

Parabolic Equations

chapter 7|34 pages

Hyperbolic Equations

chapter 8|42 pages

Elliptic Equations

chapter 9|30 pages

Spherical Harmonics

chapter 10|33 pages

Conformal Mapping Method

chapter |3 pages

A. Adjoint Operators

chapter |5 pages

B. List of Fundamental Solutions

chapter C|7 pages

C. List of Spherical Harmonics

chapter |9 pages

D. Tables of Integral Transforms

chapter |3 pages

E. Fractional Derivatives