11. As an example of an application of integral transforms , consider the Laplace transform. 12. This kernel is the kernel of integral transform . 13. This allows one to gain more insight into the nature of these integral transforms . 14. There are numerous useful integral transforms . 15. The Hankel transform is an integral transform and was first developed by the mathematician Hermann Hankel. 16. An integral transform " maps " an equation from its original " domain " into another domain. 17. The solution is then mapped back to the original domain with the inverse of the integral transform . 18. Alternatively, integral transforms , such as the hyperbolic PDE into a form of the Helmholtz equation. 19. All of the integral transforms can be expressed as linear transformations; that is, as matrices. 20. Methods of generating such expansions include the Euler Maclaurin summation formula and integral transforms such as the Mellin transforms.
