Microsoft Store
 

Laplace transform


 

In mathematics and in particular, in functional analysis, the Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:

e^{-as} F(s)

: mathcal{L}^{-1} left{ e^{-as} F(s) ight}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

◄ Laplace transform: e^{at} f(t)
Laplace transform: f(t - a) u(t - a) ►

~ Table of Content ~

►Introduction
►mathcal{L} left{f(t) ight}
►int_{0^-}^infty e^{-st} f(t),dt.
► rac{1}{2 pi imath} int_{ gamma - imath infty}^{ gamma + imath infty} e^{st} F(s),ds,
►mathcal{L}left{f(t) ight}
►int_{-infty}^{+infty} e^{-st} f(t),dt.
►s int_{0^-}^{+infty} e^{-st} f(t),dt.
►s int_{-infty}^{+infty} e^{-st} f(t),dt.
►a mathcal{L}left{ f(t) ight} +
►s mathcal{L}{f} - f(0)
►s^2 mathcal{L}{f} - s f(0) - f'(0)
►s^n mathcal{L}{f} - s^{n - 1} f(0) - cdots - f^{(n - 1)}(0)
►-F'(s)
►(-1)^{n} F^{(n)}(s)
►mathcal{L}left{ 1 * f(t) ight} {1 over s} mathcal{L}{f}
►F(s - a)
►e^{at} f(t)
►e^{-as} F(s)
►f(t - a) u(t - a)
►mathcal{L}{ f } mathcal{L}{ g }
►{1 over 1 - e^{-Ts}} int_0^T e^{-st} f(t),dt

 

 

~ What's Hot ~

The Blind Side, Avatar, Madagascar 3, All About Steve, Sex And The City 2, Ice Age Dawn Of The Dinosaurs, Harry Potter And The Half Blood Prince, Percy Jackson The Olympians The Lightning Thief, District 9, The Karate Kid, Alvin And The Chipmunks The Squeakquel, 500 Days Of Summer, The Hangover, The Mummy 4 Rise Of The Aztec, Dear John, Hannah Montana The Movie, Sorority Row, The Princess And The Frog, New Moon, Up In The Air,

~ Community ~

►History Forum
Come and discuss about History, Civilizations, Historical Events and Figures
►History Web-Ring
A community of sites, blogs and forums dedicated to History. Do not hesitate to submit your site.

Some of the information on this page come from a Wikipedia article
and are licensed under the GNU Free Documentation License.
Lexicon - Privacy Policy - Spiritus-Temporis.com ©2005.