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LT[f_,t_,s_]:=ft(*BilateralLaplaceDefined*)
∞
∫
-∞
-st
In[]:=
◻
f[t_]:=(Sin[t])*UnitStep[t]
In[]:=
Plot[f[t],{t,-10,10}]
Out[]=
In[]:=
F=LT[f[t],t,s]
☹
ConditionalExpression,Re[s]>0(*ROCdoesn'tincludejωaxis?NotStable:))
1
1+
2
s
In[]:=
Block[{s=σ+Iω},Table[plot[Abs[F],{σ,-10,10},{ω,-10,10},PlotRangeFull],{plot,{Plot3D,ContourPlot,DensityPlot}}]]
Out[]=
,
,