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B.E. CIVIL ENGINEERING,SEMESTER III,MA1201-MATHEMATICS III
Posted Date: 09 Dec 2007 Resource Type: Articles/Knowledge Sharing Category: Education
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Posted By: jegadesh Member Level: Gold
Rating:  Points: 1
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OBJECTIVES
The course objective is to develop the skills of the students in the areas of boundary value problems and transform techniques. This will be necessary for their effective studies in a large number of engineering subjects like heat conduction, communication systems, electro-optics and electromagnetic theory. The course will also serve as a prerequisite for post graduate and specialized studies and research.
1. PARTIAL DIFFERENTIAL EQUATIONS 9
Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions – Solution of standard types of first order partial differential equations – Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients.
2. FOURIER SERIES 9
Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier Series – Parseval’s identify – Harmonic Analysis.
3. BOUNDARY VALUE PROBLEMS 9
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.
4. FOURIER TRANSFORM 9
Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.
5. Z -TRANSFORM AND DIFFERENCE EQUATIONS 9
Z-transform - Elementary properties – Inverse Z – transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z - transform.
TUTORIALS 15
TOTAL : 60
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.
REFERENCES
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.
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