## 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.
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