MA6351-TRANSFORMS-AND PARTIAL DIFFERENTIAL EQUATIONS-SYLLABUS-REGULATION-2013
MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS SYLLABUS REGULATION 2013
MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS L T P C 3 1 0 4
- 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.
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.
- Veerarajan T., “Transforms and Partial Differential Equations”, Tata McGraw Hill Education
Pvt. Ltd., New Delhi, Second reprint, 2012.
- Grewal B.S., “Higher Engineering Mathematics”, 42nd Edition, Khanna Publishers, Delhi, 2012.
- Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for
Engineering Students” Vol. II & III, S.Viswanathan Publishers Pvt Ltd. 1998.
- Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 7th Edition, Laxmi Publications Pvt Ltd, 2007.
- Ramana. B.V., “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company Limited, New Delhi, 2008.
- Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education,2007.
- Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th Edition, Wiley India, 2007.
- Ray Wylie C and Barrett.L.C, “Advanced Engineering Mathematics” Tata McGraw Hill Education Pvt Ltd, Sixth Edition, New Delhi, 2012.
- Datta K.B., “Mathematical Methods of Science and Engineering”, Cengage Learning India Pvt Ltd, Delhi, 2013.
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