Curriculum
Title Special Functions & Integral Transforms (Code09010402)
Unit  Content  Learning objects  Teaching Guidelines  Methodology  Time (Hrs) 
one  Series solution of differential equations – Power series method,
Definitions of Beta and Gamma functions. Bessel equation and its solution: Bessel functions and their propertiesConvergence, recurrence, Relations and generating functions, Orthogonality of Bessel functions 
Students will be able to
1. Understand Series solution of differential equations – Power series method,
2. Bessel equation and its solution: Bessel functions and their propertiesConvergence, recurrence 3. Orthogonality of Bessel functions 
Lecture should be effective so that student can grasp the topics easily.

1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment. 
15

Two  Legendre and Hermite differentials equations and their solutions:
Legendre and Hermite functions and their propertiesRecurrence
Relations and generating functions. Orhogonality of Legendre and Hermite polynomials.
Rodrigues’ Formula for Legendre & Hermite Polynomials,Laplace
Integral Representation of Legendre polynomial. 
Students will be able to
1.Legendre and Hermite differentials equations and their solutions:
2. Relations and generating functions. Orhogonality of Legendre and Hermite polynomials.
3.Rodrigues’ Formula for Legendre & Hermite Polynomials,Laplace

Lecture should be effective so that student can grasp the topics easily.

1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment

15 
Three  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,convolution theorem, Inverse Laplace transforms of derivatives and integrals, solution of ordinary differential equations using Laplace transform.
Fourier transforms: Linearity property, Shifting, Modulation, Convolution Theorem,
Fourier Transform of Derivatives, Relations between Fourier transform and Laplacetransform,
Parseval’s identity for Fourier transforms, solution of differential Equationsusing Fourier Transforms.

To make students familiar with
Laplace Transforms – Existence theorem for Laplace transforms, Linearity of the Laplace transforms, Shifting theorems, Convolution theorem, Inverse Laplace transforms,convolution theorem, Inverse Laplace transforms of derivatives and integrals, solution of ordinary differential equations using Laplace transform. Fourier Transform of Derivatives, Relations between Fourier transform and Laplacetransform,
Parseval’s identity for Fourier transforms, solution of differential Equationsusing Fourier Transforms.

Lecture should be effective sothat student can grasp the topics easily.

1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment 
15 