TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS (AS PER ANNA UNIVERSITY SYLLABUS)
Author(s): P. Kandasamy, K. Gunavathy, Thilagavathy
Edition: 2
Publisher: S.Chand & Company
Year: 2002
Language: English
Pages: 427
1. PARTIAL DIFFERENTIAL EQUATIONS
Formation – Solutions of standard types of first order equations –
Lagrange’s Equation - Linear partial differential equations of second
and higher order with constant coefficients.
2. Fourier Series
Dirichlet’s conditions – General Fourier series – Half range Sine and
cosine series – Parseval’s identity – Harmonic Analysis.
3. Boundary value problems
Classification of second order linear partial differential equations – So-
lutions of one – dimensional wave equation, one-dimensional heat equa-
tion – Steady state solution of twodimensional heat equation – Fourier
series solution in Cartesian coordinates.
4. Laplace Transforms
Transforms of simple functions – Basic operational properties – Trans-
forms of derivatives and integrals – Initial and final value theorems –
Inverse transforms – Consvolution theorem – Periodic function – Ap-
plications of Laplace transforms of solving linear ordinary differential
equations upto second order with constant coefficients and simultaneous
equat ions of first order with constant ecoefficients.
5. Fourier Transform
Statement of Fourier integral theorem – Fourier transform pairs – Fou-
rier Sine and Consine transforms – Properties – Transforms of simple
functions – Convolution theorem – Parseval’s identity.
