181301 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Anna University Of Technology Model Question Paper

181301 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS


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1 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.

2. FOURIER TRANSFORMS

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

3. PARTIAL DIFFERENTIAL EQUATIONS

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

4. 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 conduction
(Insulated edges excluded) – Fourier series solutions in cartesian coordinates.

5. Z -TRANSFORMS AND DIFFERENCE EQUATIONS

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

TEXT BOOKS

1. Grewal, B.S, ‘Higher Engineering Mathematics’ 40th Edition, Khanna publishers,
Delhi, (2007)
3
REFERENCES
1. Bali.N.P and Manish Goyal ‘A Textbook of Engineering Mathematics’, Seventh
Edition, Laxmi Publications(P) Ltd. (2007)
2. Ramana.B.V. ‘Higher Engineering Mathematics’ Tata Mc-GrawHill Publishing
Company limited, New Delhi (2007).
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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