# MA8351-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

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1363 # MA8351-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

MA8351-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

MA8351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS                                                                                                                                              L T P C                                                                            4 0 0 4
OBJECTIVES:

• The course is designed to cover topics such as partial differential equations, Fourier series and its applications to partial differential equations, Fourier transforms and Z-transforms. This course will help the students to solve Partial Differential Equations with different methods and to introduce the application of Fourier series in solving the initial boundary value problems in one dimensional wave and heat equations and boundary value problems in elliptic equations. Also the foundations on the mathematical tools such as Fourier transforms and Z-transforms are introduced with concepts related to Engineering.

## 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 differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

## 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 – Harmonic analysis.

## 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

OUTCOMES:

After successfully completing the course, the student will have a good understanding of the following topics and their applications:

• The fundamental concepts of partial differential equations and the various solution procedures for solving the first order non-linear partial differential equations.
• Analytical methods for solving higher order partial differential equations and the application of Fourier series for solving the initial boundary value problems in one dimensional wave and heat equations and boundary value problems in elliptic equations.
• The mathematical techniques such as Fourier transforms and Z-transforms applied in various topics in engineering discipline.
• The students will gain an experience in the implementation of Mathematical concepts which are applied in various fields of Engineering.

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.