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Laplace Transform Table - Differential Equations | MTH 235, Study notes of Differential Equations

Michigan State University (MSU)Differential Equations
Prof. Gabriel Nagy

Laplace Transform Table Material Type: Notes; Professor: Nagy; Class: Differential Equations; Subject: Mathematics; University: Michigan State University; Term: Spring 2014;

Typology: Study notes

2013/2014

Uploaded on 05/02/2014

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Laplace Transform Table
f(t) = L−1(F(s)) F(s) = L(f(t))
f(n)(t) = nth derivative of f(t)F(n)(s) = nth derivative of F(s)
11
s
eat 1
s−a
tn, n = positive integer n!
sn+1
sin(at)a
s2+a2
cos(at)s
s2+a2
sinh(at)a
s2−a2
cosh(at)s
s2−a2
eatf(t)F(s−a)
tnf(t) (−1)nF(n)(s)
u(t−c)e−cs
s
u(t−c)f(t−c)e−csF(s)
f(ct)1
cF(s
c)
Rt
0f(t−τ)g(τ)dτ F (s)G(s), where [L(g(t)) = G(s)]
δ(t−c)e−cs
f(n)(t)snF(s)−sn−1f(0) −. . . −f(n−1) (0)

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Laplace Transform Table f (t) = L−^1 (F (s)) F (s) = L(f (t)) f (n)(t) = nth derivative of f (t) F (n)(s) = nth derivative of F (s) (^1 1) s eat^ s−^1 a tn, n = positive integer (^) snn+1! sin(at) (^) s (^2) +aa 2 cos(at) (^) s (^2) +sa 2 sinh(at) (^) s (^2) −aa 2 cosh(at) (^) s (^2) −sa 2 eatf (t) F (s − a) tnf (t) (−1)nF (n)(s) u(t − c) e− scs u(t − c)f (t − c) e−csF (s) f (ct) (^1) c F (sc )

∫ t

0 f^ (t^ −^ τ^ )g(τ^ )dτ^ F^ (s)G(s), where [L(g(t)) =^ G(s)] δ(t − c) e−cs f (n)(t) snF (s) − sn−^1 f (0) −... − f (n−1)(0)