TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
| L | T | P | C |
| 3 | 0 | 0 | 3 |
Laplace Transform of Standard functions, derivatives and integrals – Inverse Laplace transform –Convolution theorem-Periodic functions – Application to ordinary differential equations and simultaneous equations with constant coefficients and integral equations.
Fourier series – Dirichlet’s conditions - Half range Fourier cosine and sine series - Parseval's relation - Fourier series in complex form - Harmonic analysis.
Fourier transforms - Fourier cosine and sine transforms - inverse transforms - convolution theorem and Parseval's identity for Fourier transforms - Finite cosine and sine transforms.
Formation of partial differential equations by eliminating arbitrary constants and functions - solution of first order equations - four standard types - Lagrange’s equation - homogeneous and non-homogeneous type of second order linear differential equation with constant coefficients.
One-dimensional wave equation and one-dimensional heat flow equation - method of separation of variables - Fourier series solution.
Text Books
1. Grewal, B.S., Higher Engineering Mathematics, Khanna Publishers.
2. Kandasamy, P. Thilagavathy, K. And Gunavathy, K., Engineering Mathematics, Vol. III, Chand and Company.
3. Venkataraman, M.K., Engineering Mathematics Vol.III, National Publishing Company.
