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# Title Special Functions And Integral Transforms (Code 09050402)

#### B.Sc. (Hons) 4th semester

 S.No. Topic Domain Hours as per UGC 1 ·     Series solution of Des-Power series method ·     Definitions of Beta and Gamma functions ·     Bessel equation and its solution ·     Bessel functions and their properties-Convergence, recurrence Relations ·     Orthogonality of Bessel functions Must know 12 2 ·      Legendre and Hermite DEs and their solutions ·      Legendre and Hermite functions and their properties ·      Recurrence relations and generating functions ·      Orthogonality of Legendre and hermite polynomials ·      Rodrigues’ formula for Legendre and hermite polynomials ·      Lapalace integral representation of Legendre polynomial Must know 15 3 ·      Laplace transforms-Existence theorem for Laplace transforms ·      Linearity of the Laplace transforms, Shifting theorems ·      Laplace transforms of derivatives and integrals ·      Differentiation and integration of Laplace transforms, Convolution theorem ·      Inverse Laplace transforms of derivatives and integrals ·      Solution of ODEs using Laplace transform Must know 15 4 ·     Fourier transforms-Linearity property, Shifting, Modulation ·     Convolution Theorem ·     Fourier transform of derivatives ·     Relations between Fourier transform and Laplace transform ·     Parseval’s Identity for Fourier transforms ·     Solution of DEs using Fourier Transforms Must Know 12

Books Recommended:

1. Erwin Kreyszing : Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999
2. R. Forsyth: A Treatise on Differential Equations, Macmillan and Co. Ltd.
3. N. Sneddon: Special Functions on mathematics, Physics & Chemistry.
4. W. Bell: Special Functions for Scientists & Engineers.
5. Murray R. Spiegel: Laplace transform, Schaum’s Series