Laplace transform - Wikipedia
en.wikipedia.org › wiki › Laplace_transformIntegral transform useful in probability theory, physics, and engineering. In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace ( / ləˈplɑːs / ), is an integral transform that converts a function of a real variable. t {\displaystyle t} (often time) to a function of a complex variable. s {\displaystyle s}
Laplace transform - Wikipedia
https://en.wikipedia.org/wiki/Laplace_transform1. ^ "Differential Equations - Laplace Transforms". tutorial.math.lamar.edu. Retrieved 2020-08-08. 2. ^ Weisstein, Eric W. "Laplace Transform". mathworld.wolfram.com. Retrieved 2020-08-08. 3. ^ "Des Fonctions génératrices" [On generating functions], Théorie analytique des Probabilités [Analytical Probability Theory] (in French) (2nd ed.), Paris, 1814, chap.I sect.2-20
Differential Equations - Laplace Transforms
tutorial.math.lamar.edu › Classes › DEApr 05, 2019 · As we will see in later sections we can use Laplace transforms to reduce a differential equation to an algebra problem. The algebra can be messy on occasion, but it will be simpler than actually solving the differential equation directly in many cases. Laplace transforms can also be used to solve IVP’s that we can’t use any previous method on.
Laplace Transform: Examples - Stanford University
math.stanford.edu/~jmadnick/R3-53.pdfWe call f(t) the inverse Laplace transform of F(s) = Lff(t)g. We write f= L1fFg. Fact (Linearity): The inverse Laplace transform is linear: L 1fc 1F 1(s) + c 2F 2(s)g= c 1 L 1fF 1(s)g+ c 2 L 1fF 2(s)g: Inverse Laplace Transform: Examples Example 1: L 1 ˆ 1 s a ˙ = eat Example 2: L 1 ˆ 1 (s a)n ˙ = eat tn 1 (n 1)! Example 3: L 1 ˆ s s2 + b2 ˙ = cosbt Example 4: L 1 ˆ 1 s2 + b2 ˙ = 1 b sinbt