Integral and Discrete Transforms with Applications and Error Analysis

ISBN-13: 9780824782528 / Angielski / Twarda / 1992 / 848 str.

Abdul J. Jerri; Jerri Jerri

Opis

Describes the basic elements of integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems. This title presents background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem.

Spis treści

Part 1 Compatible transforms: the method of separation of variables and the integral 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. Part 2 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) tranforms; Laplace transform inversion; other important integral transforms. Part 3 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. Part 4 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.

O autorze

Abdul Jerri