# MA205

# 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.