Example 6.1.2

f[t_]=Piecewise[{{(t^2),0≤t<1},{(((t-1))^(-1)),1<t≤2},{1,2<t≤3}}]

Plot[f[t],{t,0,3}]

Not continuous on the interval.

Example 6.1.5

LaplaceTransform[t,t,s]

LaplaceTransform[(t^2),t,s]

LaplaceTransform[(t^n),t,s]

Example 6.1.6

LaplaceTransform[Cos[a*t],t,s]

Example 6.1.17

LaplaceTransform[t*Cosh[a*t],t,s]