Lösungen Laplace-Transformationen

?*Laplace*

?Laplace*

?InverseLaplace*

1

a

LaplaceTransform[E^(2t-3),t,s]

b

t(t-1)(t-2)//Expand

LaplaceTransform[t(t-1)(t-2)+5,t,s]

c

LaplaceTransform[Cosh[t],t,s]

d

LaplaceTransform[Sinh[t],t,s]

e

LaplaceTransform[Cosh[t] Sinh[t],t,s]

f

LaplaceTransform[2Cosh[t] -Sinh[t],t,s]

g

LaplaceTransform[Cosh[3 t],t,s]

h

LaplaceTransform[3 Cos[4 t],t,s]

i

Remove[f]

f[t_/; t < 0]:=0;
f[t_/; 0 <= t && t <= 1]:=1;
f[t_/; 1 < t]:=0;
Plot[f[t],{t,-1,2},AspectRatio->Automatic];

LaplaceTransform[f[t],t,s]

Integrate[e^(-s t) f[t],{t,0,10}]

Integrate[e^(-s t) 1,{t,0,1}]

j

D[E^(2t)*Cos[3 t]*Cosh[4 t],t]

LaplaceTransform[E^(2t)*Cos[3 t]*Cosh[4 t],t,s]

% // ExpandAll // Together

k

LaplaceTransform[Evaluate[D[E^(2t)*Cos[3 t]*Cosh[4 t],t]]
,t,s]

% // Simplify