MA 8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

UNIT I       PARTIAL DIFFERENTIAL EQUATIONS               `                           12

Formation of partial differential equations – Singular integrals – Solutions of standard types of first order partial differential equations – Lagrange’s linear equation – Linear partial differentialequations of second and higher order with constant coefficients of both homogeneous and nonhomogeneoustypes.

UNIT II      FOURIER SERIES                                                                                   12

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 – Harmonicanalysis.

UNIT III    APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS      12

Classification of PDE – Method of separation of variables – Fourier Series Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two dimensional equation of heat conduction.

UNIT IV    FOURIER TRANSFORMS                                                                     12

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                     12

Z-transforms – Elementary properties – Inverse Z-transform (using partial fraction and residues) –Initial and final value theorems – Convolution theorem – Formation of difference equations –Solution of difference equations using Z – transform.

TOTAL: 60 PERIODS

TEXT BOOKS:

1. Grewal B.S., “Higher Engineering Mathematics”, 43rd Edition, Khanna Publishers, New
Delhi, 2014.
2. Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for
Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

REFERENCES :

1. Andrews, L.C and Shivamoggi, B, “Integral Transforms for Engineers” SPIE Press, 1999.
2. Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 9th Edition, LaxmiPublications Pvt. Ltd, 2014.
3. Erwin Kreyszig, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, India,2016.
4. James, G., “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education,2007.
5. Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, NewDelhi, 2016.
6. Wylie, R.C. and Barrett, L.C., “Advanced Engineering Mathematics “Tata McGraw HillEducation Pvt. Ltd, 6th Edition, New Delhi, 2012