Engineering Mathematics Transforms and Partial Differential Equations

✍ Scribed by P. Kandasamy, K. Gunavathy, Thilagavathy

• Publisher: S.Chand & Company
• Year: 2002
• Tongue: English
• Leaves: 427
• Edition: 2
• Category: Library

✦ Synopsis

TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS (AS PER ANNA UNIVERSITY SYLLABUS)

✦ Table of Contents

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.

1. Fourier Series
   Dirichlet’s conditions – General Fourier series – Half range Sine and
   cosine series – Parseval’s identity – Harmonic Analysis.

2. 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.

3. 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.

4. 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.