# Transforms and PartiaL Differential Equations

PRE REQUISITE: Integration, Concept of continuity,differentiability, etc.

Faculty :Dr.Gomathinayagam

OBJECTIVE: After completing the course , a student will be able to solve problems in Partial DifferentialEquations.(Wave equation and Heat equation)

1.LAPLACE TRANSFORMS (8)
Laplace Transform of Standard functions, derivatives and integrals ÃƒÂ¯Ã‚Â¿Ã‚Â½ Inverse Laplace transform ÃƒÂ¯Ã‚Â¿Ã‚Â½Convolution theorem-Periodic functions ÃƒÂ¯Ã‚Â¿Ã‚Â½ Application to ordinary differential equations and simultaneous equations with constant coefficients and integral equations.

2. FOURIER SERIES (8)
DirichletÃƒÂ¯Ã‚Â¿Ã‚Â½s conditions - Half range Fourier cosine and sine series - Parseval's relation - Fourier series in complex form - Harmonic analysis.

3. FOURIER TRANSFORMS (8)
Fourier cosine and sine transforms - inverse transforms - convolution theorem and Parseval's identity for Fourier transforms - Finite cosine and sine transforms.

4. FORMATION OF PARTIAL DIFF EQUATIONS (8)
By eliminating arbitrary constants and functions - solution of first order equations - four standard types - LagrangeÃƒÂ¯Ã‚Â¿Ã‚Â½s equation - homogeneous and non-homogeneous type of second order linear differential equation with constant coefficients.

5.ONE DIMENSIONAL WAVE EQUATION (8)
One-dimensional wave equation and one-dimensional heat flow equation - method of separation of variables - Fourier series solution.

TEXT BOOKS

1. Churchill,R .V.,"Fourier Series and Boundary Value Problems", McGraw Hill, New Delhi,1995.

2 Kandasamy,P. "Engineering Mathematics", Vol III, S Chand & Co., 1996.

3. Venkataraman, M.K, "Engineering Mathematics", Third year Part A, NPC, 1995.

REFERENCES

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.