# 301

# BEE301 FOURIER SERIES AND APPLICATIONS

OBJECTIVE: To solve problems using Fourier series, Fourier transforms and partial differential equations.

## 1. LAPLACE EQUATION:

Transform of Standard function,Unit and Step function,Dirac delta function - Transform of derivatives and Integrals - Inverse Laplace transform - Convolution theorem - Periodic functions - Application to ordinary differential equations and simultaneous equations with constant coeffiecients, and integral equations.

## 2. FOURIER SERIES:

Dirichlet's conditions and general Fourier series with period 2L - Half range Fourier cosine and sine series - Parseval's relation - Fourier series in complex form - Harmonic analysis.

3. FOURIER TRANSFORMS:

Fourier transforms - Fourier cosine and sine transforms - inverse transforms - convolution theorem and parseval's identity for Fourier transforms - finite cosine and sine transforms.

## 4. PARTIAL DIFFERENTIAL EQUATIONS:

Formation of partial differential equations eliminating arbitrary constants and functions - solution of first order equations - four standard types - Lagrange's equation - homogeneous and non-homogeneous type of second order linear differential equation with constant coefficients.

## 5. WAVE EQUATION AND ONE DIMENSIONAL HEAT FLOW EQUATION:

Derivations of one-dimensional wave equation and one-dimensional heat flow equation - method of separation of variables - Fourier series solution.