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- W589060377 abstract "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." @default.
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- W589060377 date "1992-06-11" @default.
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- W589060377 title "Integral and Discrete Transforms with Applications and Error Analysis" @default.
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