## Quick Reference

A relationship between two or more functions can be expressed in the form *f* (*x*)=∫*K* (*x*, *y*) *F*(*X*) *dy* then *f*(*x*) is the integral transform of *F*(*x*), and *K*(*x, y*) is the kernel of the transform. If *F*(*x*) can be found from *f*(*x*) then the transform can be inverted. Integral transformations are particularly useful where they result in simplifying equations into forms where methods of solution are much easier. For example, differential equations can be reduced to linear equations where the solution is straightforward, and when the inverse transform also exists the solution to the original problem can be obtained. Fourier and Laplace transformations are examples of integral transformations.

*Subjects:*
Mathematics.