3-1-MA6351-Transforms and Partial Differential Equations

General info: MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL	University – Anna university, Tamil nadu, India Marks: UNIT 1 to 5 – 9+3 each unit  Period - TOTAL (L:45+T:15): 60 PERIODS
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   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 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   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   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 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.
TEXT BOOKS:  1) Veerarajan. T., "Transforms and Partial Differential Equations", Tata McGraw Hill Education Pvt. Ltd., New Delhi, Second reprint, 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. 2. Ramana.B.V., "Higher Engineering Mathematics", Tata Mc Graw Hill Publishing Company Limited, NewDelhi, 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 Mc Graw 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.
Notes from :UNIT-1, UNIT-2, UNIT-3, UNIT-4, UNIT-5 NOTES FROM VIDHYARTHI: CLICK HERE