Fourier Series

Jose StewartAdvised by Dr. Netra KhanalThe University of TampaApril 2013Fourier Series

Partial Differential EquationsDifferential equations arise in many areas of science and technology, where continuously variable quantities and their rates of change are related.

ODE-Equation for unknown function which relates values of functions and its derivates of various orders.

PDE-Differential Equation involving multivariable functions and their partial derivates.

Fourier SeriesFourier introduced series for the purpose of solving the heat equation through a metal plateMethod involves expressing a function as an infinite sum of sines and/or cosines

Periodicity of Sine and CosineA function is periodic with period T>0 if the domain of the function contains (x+T) when containing x and if

Also, if T is a period of a function, then any integral multiple of T is also a period. The smallest value of T for which the above equation holds is called the fundamental period of the given function.

Orthogonality of Sine and cosineThe standard inner product (u,v) of two real valued functions with ( x ) is given by

The functions u and v are said to be orthogonal if

A set of functions is said to be mutually orthogonal if each distinct pair of functions in the set is orthogonal.

The functions sin(mx/L) and cos(mx/L), m=1,2,3 form a mutually orthogonal set of functions on the interval L