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Transform (mathematics)
From Wikipedia, the free encyclopedia
In mathematics a transform is an operator applied to a function so that under the transform certain operations are simplified. For example, in arithmetic when finding the logarithm of numbers, the process of finding the logarithm of the product is reduced to the simpler process of adding the logarithms of each factor. We may then regard the operation of taking the logarithms as a transform that turns numbers into other numbers, and in doing so it makes some aspect of the calculation easier.[1]
In higher mathematics this idea is applied to functions in order to solve certain types of differential equations. For example, the Laplace transform is the operation of multiplying a function F(t) of the real variable t, defined for t > 0, by exp(-pt) where p is a complex variable x + iy, and then integrating the result, with respect to t, from zero to infinity. This generates a new function f(p) called the Lapalce transform of F(t). Under this transform the solutions to some differential equations are are greatly simplified.[1]
Another type of transform used to simply the process of solving differential equations is called the Fourier transform.[1]