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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