Previous years Anna University Questions were uploaded fro the subject of MA6351 Transforms and Partial Differential Equations which is given by the Anna University to the All Engineering departments except Environmental Engineering, Textile Technology,Textile chemistry, Fashion Technology and Pharmaceutical Technology.
The syllbus of MA6351-Transforms and Partial Differential Equations also given in this post see after the question.
B.E/B.Tech DEGREE EXAMINATION,NOVEMBER/DECEMBER 2014
Third Year
Civil Engineering
MA6351-Transforms and Partial Differential Equations
(Common to all branches except Environmental Engineering, Textile Technology,Textile chemistry, Fashion Technology and Pharmaceutical Technology)
MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS L T P C
3 1 0 4
OBJECTIVES
To introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems.
To acquaint the student with Fourier transform techniques used in wide variety of situations.
To introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time
systems.
UNIT I PARTIAL DIFFERENTIAL EQUATIONS 9 + 3
Formation of partial differential equations – Singular integrals -- Solutions 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 of both homogeneous and non-homogeneous types.
UNIT II FOURIER SERIES 9 + 3
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 identity – Harmonic analysis.
UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 9 + 3
Classification of PDE – Method of separation of variables - Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction (excluding insulated edges).
UNIT IV FOURIER TRANSFORMS 9 + 3
Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.
UNIT V Z - TRANSFORMS AND DIFFERENCE EQUATIONS 9 + 3
Z- transforms - Elementary properties – Inverse Z - transform (using partial fraction and residues) – Convolution theorem - Formation of difference equations – Solution of difference equations using Z - transform.
OUTCOMES
TOTAL (L:45+T:15): 60 PERIODS
The understanding of the mathematical principles on transforms and partial differential equations would provide them the ability to formulate and solve some of the physical problems of engineering.
TEXT BOOKS
1. Veerarajan. T., "Transforms and Partial Differential Equations", Tata McGraw Hill Education
Pvt. Ltd., Second reprint, New Delhi, 2012.
2. Grewal. B.S., "Higher Engineering Mathematics", 42nd Edition, Khanna Publishers, Delhi,
2012.
3. Narayanan.S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for
Engineering Students" Vol. II & III, S.Viswanathan Publishers Pvt Ltd. 1998.
REFERENCES
1. Bali.N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 7th Edition, Laxmi
Publications Pvt Ltd, 2007.
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