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# 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

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.

TOTAL (L:45+T:15): 60 PERIODS

OUTCOMES:

• 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., New Delhi, Second reprint, 2012.

1. Grewal B.S., “Higher Engineering   Mathematics”, 42nd     Edition, Khanna Publishers, Delhi, 2012.
1. 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.
2. Ramana. B.V., “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company  Limited, New Delhi, 2008.
3. Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education,2007.
4. Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th Edition, Wiley India, 2007.
5. Ray Wylie  C  and  Barrett.L.C,  “Advanced  Engineering  Mathematics”  Tata    McGraw  Hill Education Pvt Ltd, Sixth Edition, New Delhi, 2012.
6. Datta K.B., “Mathematical Methods of Science and Engineering”, Cengage Learning India Pvt Ltd,  Delhi, 2013.