In[]:=
f[t_]:=UnitStep[t+1]
In[]:=
Plot[f[t],{t,-10,10}]
Out[]=
In[]:=
F=LT[UnitStep[t+2],t,s]
Out[]=
ConditionalExpression
2s

s
,Re[s]>0
​
In[]:=
Block[{s=σ+Iω},Table[plot[Abs[F],{σ,-20,20},{ω,-20,20},PlotRangeFull],{plot,{Plot3D,ContourPlot,DensityPlot}}]]
Out[]=

,
,
