- Transform (mathematics)
In
mathematics a transform is anoperator applied to a function so that under the transform certain operations are simplified. For example, in arithmetic when finding thelogarithm of numbers, the process of finding the logarithm of theproduct 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."Transform Calculus: with an Introduction to Complex Variables" by E. J. Scott]In higher mathematics this idea is applied to functions in order to solve certain types of
differential equations . For example, theLaplace 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 acomplex 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 "Laplace transform " of F(t). Under this transform the solutions to some differential equations are greatly simplified."Transform Calculus: with an Introduction to Complex Variables" by E. J. Scott]Another type of transform used to simplify the process of solving differential equations is called the
Fourier transform ."Transform Calculus: with an Introduction to Complex Variables" by E. J. Scott]ee also
*
List of transforms
*Fourier analysis
*Transform theory References
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