Laplace transform of derivative
Theorem. If the real function and its derivative are Laplace-transformable and is continuous for , then
(1) |
Proof. By the definition of Laplace transform and using integration by parts, the left hand side of (1) may be written
The Laplace-transformability of implies that tends to zero as increases boundlessly. Thus the last expression leads to the right hand side of (1).
Title | Laplace transform of derivative |
---|---|
Canonical name | LaplaceTransformOfDerivative |
Date of creation | 2013-03-22 18:24:54 |
Last modified on | 2013-03-22 18:24:54 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 5 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 44A10 |
Related topic | SubstitutionNotation |