MA2211 Transforms and Partial Differential Equations - SUBJECT CATALOG

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SYLLABUS:

MA2211	TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS	L T  P C
	(Common to all branches)	3   1  0 4

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    9

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      9

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    9

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    9

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         9

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.