MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

(Common to all branches)

OBJECTIVES

The course objective is to develop the skills of the students in the areas of Transforms and Partial
Differtial Equations. This will be necessary for their effective studies in a large number of engineering
subjects like heat conduction, communication systems, electro-optics and electromagnetic theory.
The course will also serve as a prerequisite for post graduate and specialized studies and research.

UNIT I 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 identify – Harmonic Analysis.

UNIT II FOURIER TRANSFORM

Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s
identity.

UNIT III PARTIAL DIFFERENTIAL EQUATIONS 

Formation of partial differential equations - Lagrange’s linear equation - Solution of standard types
of first order partial differential equations – Linear partial differential equations of second and higher
order with constant coefficients.

UNIT IV APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 

Solutions of one dimensional wave equation – One dimensional equation of heat conduction –
Steady state solution of two-dimensional equation of heat equation (Insulated edges excluded) –
Fourier series solutions in cartesian coordinates.

UNIT V Z -TRANSFORM AND DIFFERENCE EQUATIONS

Z-transform - Elementary properties – Inverse Z – transform – Convolution theorem -Formation of
difference equations – Solution of difference equations using Z - transform.

TUTORIALS = 15 TOTAL = 60 PERIODS

TEXTBOOKS

1. Grewal B.S, ‘Higher Engineering Mathematics’, 39th Edition, Khanna Publishers, Delhi, 2007.

REFERENCE:

1. Bali.N.P. and Manish Goyal ‘A Textbook of Engineering Mathematics’, Seventh Edition, Laxmi
Publications (P) Ltd.
2. Ramana.B.V. ‘Higher Engineering Mathematics’ Tata Mc-GrawHill Publishing Company Limited,
New Delhi.
3. Glyn James ‘ ADVANCED MODERN ENGINEERING MATHEMATICS’, Third edition – Pearson
education – 2007.
4. ERWIN KREYSZIG ‘ ADVANCED ENGINEERING MATHEMATICS’ Eighth Edition – WILEY
INDIA – 2007.