Publisher:

Chapman & Hall/CRC

Number of Pages:

356

Price:

119.95

ISBN:

9781439840085

Date Received:

Thursday, February 3, 2011

Reviewable:

No

Reviewer Email Address:

Series:

Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series

Publication Date:

2011

Format:

Hardcover

Audience:

Category:

Textbook

**Some Basic Results**Euclidean Space

Classes of Continuous Functions

Convergence

Functionals

Linear Transformations

Cramer’s Rule

Green’s Identities

Differentiation and Integration

Inequalities

**The Concept of Green’s Functions**Generalized Functions

Singular Distributions

The Concept of Green’s Functions

Linear Operators and Inverse Operators

Fundamental Solutions

**Sturm–Liouville Systems**Ordinary Differential Equations

Initial Value Problems

Boundary Value Problems

Eigenvalue Problem for Sturm–Liouville Systems

Periodic Sturm–Liouville Systems

Singular Sturm–Liouville Systems

**Bernoulli’s Separation Method **Coordinate Systems

Partial Differential Equations

Bernoulli’s Separation Method

Examples

**Integral Transforms **Integral Transform Pairs

Laplace Transform

Fourier Integral Theorems

Fourier Sine and Cosine Transforms

Finite Fourier Transforms

Multiple Transforms

Hankel Transforms

Summary: Variables of Transforms

**Parabolic Equations**1-D Diffusion Equation

2-D Diffusion Equation

3-D Diffusion Equation

Schrödinger Diffusion Operator

Min-Max Principle

Diffusion Equation in a Finite Medium

Axisymmetric Diffusion Equation

1-D Heat Conduction Problem

Stefan Problem

1-D Fractional Diffusion Equation

1-D Fractional Schrödinger Diffusion Equation

Eigenpairs and Dirac Delta Function

**Hyperbolic Equations**1-D Wave Equation

2-D Wave Equation

3-D Wave Equation

2-D Axisymmetric Wave Equation

Vibrations of a Circular Membrane

3-D Wave Equation in a Cube

Schrödinger Wave Equation

Hydrogen Atom

1-D Fractional Nonhomogeneous Wave Equation

Applications of the Wave Operator

Laplace Transform Method

Quasioptics and Diffraction

**Elliptic Equations**Green’s Function for 2-D Laplace’s Equation

2-D Laplace’s Equation in a Rectangle

Green’s Function for 3-D Laplace’s Equation

Harmonic Functions

2-D Helmholtz’s Equation

Green’s Function for 3-D Helmholtz’s Equation

2-D Poisson’s Equation in a Circle

Method for Green’s Function in a Rectangle

Poisson’s Equation in a Cube

Laplace’s Equation in a Sphere

Poisson’s Equation and Green’s Function in a Sphere

Applications of Elliptic Equations

**Spherical Harmonics **Historical Sketch

Laplace’s Solid Spherical Harmonics

Surface Spherical Harmonics

**Conformal Mapping Method**Definitions and Theorems

Dirichlet Problem

Neumann Problem

Green’s and Neumann’s Functions

Computation of Green’s Functions

** **

**Appendix A: Adjoint Operators****Appendix B: List of Fundamental SolutionsAppendix C: List of Spherical Harmonics**

**Bibliography**

**Index**

Publish Book:

Modify Date:

Wednesday, July 13, 2011

- Log in to post comments