**MA8353** **TPDE Syllabus**

Anna University Regulation 2017 EEE** MA8353 TPDE Syllabus for all 5 units** are provided below. Download link for **EEE 3RD SEM MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus** is listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 ELECTRICAL AND ELECTRONICS ENGINEERING (EEE) 3RD SEM MA8353 TPDE – TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Syllabus

MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS ENGINEERING L T P C 3 0 0 3

OBJECTIVES:

- To introduce the basic concepts of PDE for solving standard partial differential equations.
- 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 series techniques in solving heat flow problems used in

various situations.

- 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 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 :

Upon successful completion of the course, students should be able to:

- Understand how to solve the given standard partial differential equations.
- Solve differential equations using Fourier series analysis which plays a vital role in engineering

applications.

- Appreciate the physical significance of Fourier series techniques in solving one and two

dimensional heat flow problems and one dimensional wave equations.

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- Understand 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.

- Use the effective mathematical tools for the solutions of partial differential equations by using

Z transform techniques for discrete time systems.

TEXT BOOKS :

- Grewal B.S., “Higher Engineering Mathematics”, 43rd Edition, Khanna Publishers, New Delhi,

2014.

- 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 :

- Andrews, L.C and Shivamoggi, B, “Integral Transforms for Engineers” SPIE Press, 1999.
- Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 9th Edition, Laxmi

Publications Pvt. Ltd, 2014.

- Erwin Kreyszig, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, India, 2016.
- James, G., “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2007.
- Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi,

2016.

- 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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MA8353 Syllabus, TPDE Unit wise Syllabus – EEE 3RD Semester