ABSTRACT
Integral Transforms provide a strong and effective mathematical tool for the solution of diverse problems in science and engineering. Euler developed the technique of using integral transform for the solution of differential equations in 1769. Many mathematicians and physicists contributed to its development and extension over time. Now there are dozens of integral transforms, many of which are related to particular types of functions such as sine or cosine functions, exponential functions, and Bessel functions. In this chapter, we will briefly discuss a few more important types of transforms – (1) complex Fourier transform or simply Fourier transform, (2) Fourier sine and cosine transforms, (3) finite Fourier sine and cosine transforms, and (4) Laplace transform and will show a few applications in solution of real life problems. The Mellin and Hankel transforms* will be just defined. Application of the transform techniques covers many physical, engineering and other disciplines, but we will confine ourselves to the areas relevant to chemical engineering. Since Laplace transform has been more widely used to solve chemical engineering problems, we will discuss it in considerable detail and show its applications in the solution of transport problems of heat and mass, especially in relation to diffusion-reaction, controlled drug release and environmental dispersion. First, we will take a brief look into the origin of the transforms and their selected properties rather than using them straightaway for the solution of problems.
