MA1201--MATHEMATICS III - Syllabus - Reg 2004

MA1201--MATHEMATICS III

PARTIAL DIFFERENTIAL EQUATIONS

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions - Solution of standard types of first order partial differential equations - Lagranges linear equation - Linear partial differential equations of second and higher order with constant coefficients.

FOURIER SERIES

Dirichlets conditions - General Fourier series - Odd and even functions - Half range sine series - Half range cosine series - Complex form of Fourier Series - Parsevals identify - Harmonic Analysis.

BOUNDARY VALUE PROBLEMS

Classification of second order quasi linear partial differential equations - Solutions of one dimensional wave equation - One dimensional heat equation - Steady state solution of two-dimensional heat equation (Insulated edges excluded) - Fourier series solutions in Cartesian coordinates.

FOURIER TRANSFORM

Fourier integral theorem (without proof) - Fourier transform pair - Sine and Cosine transforms - Properties - Transforms of simple functions - Convolution theorem - Parsevals identity.

Z -TRANSFORM AND DIFFERENCE EQUATIONS

Z-transform - Elementary properties - Inverse Z - transform - Convolution theorem -Formation of difference equations - Solution of difference equations using Z - transform.

Reference

Text Books

1. Grewal, B.S., -Higher Engineering Mathematics Thirty Sixth Edition , Khanna Publishers, Delhi, 2001. 2. Kandasamy, P., Thilagavathy, K., and Gunavathy, K., -Engineering Mathematics Volume III S. Chand & Company ltd., New Delhi, 1996. 3. Wylie C. Ray and Barrett Louis, C., -Advanced Engineering Mathematics Sixth Edition, McGraw-Hill, Inc., New York, 1995.

Reference Books

1. Andrews, L.A., and Shivamoggi B.K., -Integral Transforms for Engineers and Applied Mathematicians,- Macmillen, New York, 1988. 2. Narayanan, S., Manicavachagom Pillay, T.K. and Ramaniah, G., -Advanced Mathematics for Engineering Students Volumes II and III, S. Viswanathan (Printers and Publishers) Pvt. Ltd. Chennai, 2002. 3. Churchill, R.V. and Brown, J.W., -Fourier Series and Boundary Value Problems Fourth Edition, McGraw-Hill Book Co., Singapore, 1987.