This document outlines the syllabus for a course on Transforms and Partial Differential Equations. It includes 5 units that cover various topics: Fourier transforms and their properties; Z-transforms and difference equations; Fourier series; boundary value problems involving partial differential equations; and formation and solutions of partial differential equations of various orders with constant coefficients. Recommended textbooks for the course are also listed.

1. MUTHAYAMMAL ENGINEERING COLLEGE
MUTHAYAMMAL ENGINEERING COLLEGE
RASIPURAM
RASIPURAM
TRANSFORMS & PARTIAL DIFFERENTIAL
EQUATIONS
19BSS23
Prepared by : Department of
Mathematics

2. SYLLABUS
SYLLABUS
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UNIT – I FOURIER TRANSFORMS
Statement of Fourier integral theorem - Fourier transforms pair – Fourier sine and cosine
transforms – Properties – Transforms of simple functions – Convolution theorem –
Parseval’s identity–Problems .
UNIT – II Z - TRANSFORMS AND DIFFERENCE EQUATIONS
Z- transforms - Elementary properties – Initial and final value theorem – Inverse Z - transforms –
Partial fraction method – Residue method – Convolution theorem - Formation of difference
equations – Solution of difference equations using Z – transforms
UNIT - III FOURIER SERIES
Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series
– Half range cosine series – Parseval’s identity – Harmonic analysis
UNIT – IV BOUNDARY VALUE PROBLEMS
Classification of PDE - Solutions of one dimensional wave equation – One dimensional equation
of heat conduction – Fourier series solution in Cartesian coordinates – Steady state solution of
two dimensional equation of heat conduction (excluding insulated edges) on finite square plates
(excluding circular plates).
UNIT – V PARTIAL DIFFERENTIAL EQUATIONS
Formation of partial differential equations – Singular integrals – Solutions of standard types of
first order partial differential equations – Lagrange’s linear equation - Linear partial differential
equations of second and higher order with constant coefficients of homogeneous when the R.H.S
is eax+by , xm yn m,n>0, sin (ax+by), cos (ax+by)

3. Text Books:
Text Books:
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Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition,
John Wiley and Sons, New Delhi-2014.
Grewal. B.S, Higher Engineering Mathematics, 43rd Edition, Khanna
Publications, Delhi-2014.

37. Z-Transforms and Difference Equations

71. Fourier Series

86. APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATION

94. 1