释义 |
Laplace transform An integral transform ℒ of a function f(x) into another function ℒf or of a different variable p. The Laplace transform of f(x) is defined as

The transform is useful in solving differential equations, as it handles derivatives well; for example, the transform of f′(x) equals . At its simplest, a differential equation in f(x) is transformed into an algebraic equation involving which is solved to find ; by recognizing as the transform of a function, or by applying an inverse transform theorem, the solution f(x) can then be found. For a list of Laplace transforms, see appendix 10. See also Fourier transform. |