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# Syllabus | B.Sc (Non- Medical) | Title- Special Functions & Integral Transforms (Code-09010402)

### Title- Special Functions & Integral Transforms (Code-09010402)

 S.No Unit Contents Domain Time(H) 1 One 1.   Series solution of Des-Power series method 2.   Definitions of Beta and Gamma functions 3.   Bessel equation and its solution 4.   Bessel functions and their properties 5.   Relations and generating functions 6.   Orthogonality of Bessel functions Must know Nice to know 10 2 Two 1.   Legendre and Hermite DEs and their solutions 2.   Legendre and Hermite functions and their properties 3.   Recurrence relations and generating functions 4.   Orthogonality of Legendre and hermite polynomials 5.   Rodrigues’ formula for Legendre and hermite polynomials 6.   Lapalace integral representation of Legendre polynomial 7.   Laplace transforms, 8.   Existence theorem for Laplace transforms 9.   Linearity of the Laplace transforms, 10.  Shifting theorems, Convolution theorem 11.  Laplace transforms of derivatives and integrals 12.  Differentiation and integration of Laplace transforms 13.  Inverse Laplace transforms 14.  Solution of ODEs using Laplace transform Must know 28 3 Three 1.   Fourier transforms-Linearity property, Shifting, Modulation 2.   Convolution Theorem 3.   Fourier transform of derivatives 4.   Relations between Fourier transform and Laplace transform 5.   Parseval’s Identity for Fourier transforms 6.   Solution of DEs using Fourier Transforms Must know   Nice to know 12