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The Maxima on-line user's manual

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Unit_step

Function: unit_step (<x>) The left-continuous unit step function; thus unit_step (<x>) vanishes for <x> <= 0 and equals 1 for <x> > 0.

f(t):=cos(3*t);
g(t):=f(t-1)*unit_step(t-1);
laplace(g(t),t,s);
plot2d(g(t),[t,-1,1],[y,-2,2]);

If you want a unit step function that takes on the value 1/2 at zero, use (1 + signum (<x>))/2.

(%o1)                                true
(%i2) 

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