MA8353 Transforms And Partial Differential Equations Notes Syllabus Question Bank Regulation 2017

MA8353 Transforms And Partial Differential Equations   Lecture Notes Syllabus Book Previous  2 13 15 Marks  Anna University Important Question Bank With Answers  Regulation 2017 Study Materials Pdf Ppt

MA8353 Transforms And Partial Differential Equations

MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

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 nonhomogeneous 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 - 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 

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) – Initial and final value theorems - Convolution theorem - Formation of difference equations – Solution of difference equations using Z - transform.

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, Laxmi Publications 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, New Delhi, 2016.

6. Wylie, R.C. and Barrett, L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.

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