TRANSFORM & PARTIAL DIFFERENTIAL EQUATIONS

520 364

First Edition :June 2016

Second Edition : April 2017

Third New Edition :June 2018

Fourth Revised Edition :July 2019

Fifth Edition “July 2022

ISBN :978-93-85374-43-2

UNIT I :  PARTIAL DIFFERENTIAL EQUATIONS

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

UNIT II : FOURIER SERIES

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series and cosine series – Root mean square value – Parseval’s identity – Harmonic analysis.

UNIT III : APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

Classification of PDE – Method of separation of variables – Fourier series solutions of one-dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two- dimensional equation of heat conduction (Cartesian coordinates only).

UNIT IV :  FOURIER TRANSFORMS

Statement of Fourier integral theorem– Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

UNIT  V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS

Z-transforms – Elementary properties – Convergence of Z-transforms – – Initial and final value theorems – Inverse Z-transform using partial fraction and convolution theorem – Formation of difference equations – Solution of difference equations using Z – transforms.

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