181301 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

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.

FOURIER TRANSFORMS

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

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.

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.

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)

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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