Title- Special Functions And Integral Transforms (Code-09050402)
S.No. | Contents of the topics | Learning Objectives | Teaching Guidelines | Methodology | Time
(Hour) |
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 |
Students will be able to understand Study of series solution of DEs and Bessel’s equations with its properties | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations |
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 |
Students will be able to understand Study of Legendre and Hermite DEs and polynomials | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations |
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 |
Students will be able to understand Study of Laplace Transforms with its properties | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations |
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 |
Students will be able to understand Study of Fourier Transforms with its properties | Lecture should be effective so that student can grasp the topics easily | Assignments/ seminars/ Class tests/ Presentations | 10 |
Books Recommended:
- Erwin Kreyszing : Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999
- R. Forsyth: A Treatise on Differential Equations, Macmillan and Co. Ltd.
- N. Sneddon: Special Functions on mathematics, Physics & Chemistry.
- W. Bell: Special Functions for Scientists & Engineers.
- Murray R. Spiegel: Laplace transform, Schaum’s Series