MA2211-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS - Anna University 2008 regulation

MA2211-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.

REFERENCE

Text Books

1.Grewal, B.S, ‘Higher Engineering Mathematics’ 40th Edition, Khanna publishers, Delhi,(2007).

Reference Books

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).