A Study on Some Integral Transforms Used in Engineering Sciences

Abstract

Transform methods, have their great importance in the field of applied sciences especially in engineering sciences, are divided in two categories continuous and discrete, of which our matter of interest is the continuous one. To most of us, Laplace transform a member of the continuous transform category is well known and we are acquainted to solve differential equations with this important tool. The procedure of adopting a transform consists of three steps- use of the transform, algebraic manipulation and finally inversion. In case of Laplace transform the inversion with the definition is not usually an adopted one, but is a powerful tool. In this study we have rigorously handled the Laplace transform and complex inversion formula is utilized to obtain the inverse. Hankel transform, another member of the same category which has specialty in handling cylindrical coordinates with circular symmetry is also studied. It has been observed that when periodic, impulsive or similar forces are applied to a system, is is not that much difficult to obtain the solution of the system when complex inversion formula is used while Laplace transform method is used as a solving tool. Thus as a concluding remark, it has been suggested to pay proper attention to the complex inversion formula.