Table of Laplace Transforms Last updated Jan 17, 2020 Save as PDF Table of Integrals Florida SouthWestern State College Page ID33424 ( \newcommand{\kernel}{\mathrm{null}\,}\) Table of Laplace Transforms f(t)=L−1{F(s)} F(s)=L{F(s)} f(t)=L−1{F(s)} F(s)=L{F(s)} 1.1 1s 2.t 1s2 3.tn,n=1,2,3,⋯ n!sn+1 4.eat 1s−a 5.sinat as2+a2 6.cosat ss2+a2 7.sinhat as2−a2 8.coshat ss2−a2 9.eat⋅f(t) F(s−a) Unit Step or Heavyside Function 10.U(t−a) e−ass 11.f(t−a)⋅U(t−a) e−as⋅F(s) 12.f(t)⋅U(t−a) e−as⋅L{f(t+a)} 13.f′(t) sF(s)−f(0) 14.f″(t) s2F(s)−s⋅f(0)−f′(0) 15.t⋅f(t) −F′(s) 16.f(n)(t) snF(s)−s(n−1)f(0)−⋯ −sf(n−2)(0)−f(n−1)(0) 17.tn⋅f(t) (−1)ndndsn(F(s)) 18.1t⋅f(t) ∫∞sF(w)dw Dirac Delta Function 19.δ(t−a) e−as Convolution 20.f(t)∗g(t) F(s)⋅G(s) Dirac Delta Function 21.δ(t−a)f(t) f(a)⋅e−as Periodic function with period T 22.f(t+T)=f(t) FT(s)1−e−Ts=∫T0e−stf(t)dt1−e−Ts