chapter  1
78 Pages

Fourier Transform

ByBaidyanath Patra

The method of integral transforms is one of the most easy and effective methods for solving problems arising in Mathematical Physics, Applied Mathematics and Engineering Science which are defined by differential equations, difference equations and integral equations. The main idea in the application of the method is to transform the unknown function, say, f(t) of some variable t to a different function, say, F(p) of a complex variable p. Then the associated differential equation can be directly reduced to either a differential equation of lower dimension or an algebraic equation in the variable p. There are several forms of integral transforms and one form may be obtained from the other by a transformation of the coordinates and the functions. The choice of integral transform depends on the structure of the equation and on the geometry of the domain under consideration. This method of integral transform simplifies the computational techniques considerably.