Integral and Discrete Transforms With Applications and Error Analysis

                                                                                                Hardcover
                                                                                                Published by Marcel Dekker
                                                                                                Publication date: 1992, 848p.
                                                                                                ISBN: 0824782526
 
 

This useful reference/text describes the basic elements of the integral, finite, and discrete boundary and initial value problems as well as facilitating the representations of signals and systems.

Proceeding to the final solution in the same setting of Fourier analysis without interruption. Integral and Discrete Transforms with Applications and Error Analysis…

• presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem
• discusses modeling of the basic partial differential equations, as well as the solutions in terms of the main special functions
• considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method
• covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems
• examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred
• and more!

Table of Contents

Compatible Transforms
The Method of Separation of Variables and the Integral Transforms Compatible Transforms
Compatible Transforms
Classification of the Transforms
Comments on the Inverse Transforms-Tables of the Transforms
The Compatible Transform and the Adjoint Problem
Constructing the Compatible Transforms for Self-Adjoint Problems- Second-Order Differential Equations
The nth-Order Differential Operator
Integral Transforms
Laplace Transforms
Fourier Exponential Transforms
Boundary and Initial Value Problems- Solutions by Fourier Transforms
Signals and Linear Systems- Representation in the Fourier ( Spectrum ) Space
Fourier Sine and Cosine Transforms
Higher? Dimensional Fourier Transforms
The Hankel ( Bessel ) Transforms
Laplace Transform Inversion
Other Important Integral Transforms
Finite Transforms- Fourier Series and Coefficients
Fourier ( Trigonometric ) Series and General Orthogonal Expansion
Fourier Sine and Cosine Transforms Fourier ( Exponential ) Transforms
Hankel ( Bessel ) Transforms
Classical Orthogonal Polynomial Transforms
The Generalized Sampling Expansion
A Remark on the Transform Methods and Nonlinear Problems
Discrete Transforms
Discrete Fourier Transforms
Discrete Orthogonal Polynomial Transforms
Bessel-type Poisson Summation Formula ( for the Bessel? Fourier Series and Hankel Transforms)

Appendix A:Basic Second-Order Differential Equations and Their ( Series ) Solutions ? Special Functions

Appendix B:Mathematical Modeling of Partial Differential Equations ? Boundary and Initial Value Problems

Appendix C:Tables of Transforms

Index of Notation
 
 

June 1992, 848 p.
ISBN: 0824782526
USD 225.00
USD 75.00 on orders of five or more copies, for classroom use only

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