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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

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