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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 수리분석
· ISBN : 9780824782528
· 쪽수 : 848쪽
목차
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.