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The Maxima on-line user's manual

Algebra Calculator

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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.

u(t,x):=sum(9*sin(%pi*n/3)*sin(n*%pi*x/30)*cos(n*%pi*t/15)/(n^2*%pi^2),n,1,3);
T:makelist(i*2,i,1,9);
f(x):=x/10+unit_step(x-10)*(-x/10+(30-x)/20);
plot2d([f(x),u(x,T)],[x,0,30]);

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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