principles of delayed exponential function and laplace transformation
and unit step function (heaviside)
peter.vlasschaert@gmail.com,09/10/2017          (17.10 version maxima)

kill(all)$
load(orthopoly)$                        /*we get otherwise warning text*/

p1:wxplot2d([3*unit_step(x-1)-3*unit_step(x-2)],[x,-2,5], [y,-5,5])$

p2:wxplot2d([3*unit_step(x-2)-3*unit_step(x-3)], [x,-2,5],[y,-5,5])$

p3:wxplot2d([3*unit_step(x-1)*sin(x-1),3*unit_step(x-1)],[x,-2,5], [y,-5,5])$

p4:f(t):=5*exp(-0.3*t)$

p5:wxplot2d([f(x),5*unit_step(x-2)], [x,-5,5],[y,-10,10])$

laplace transform of a delayed exponential function

p6:wxplot2d([f(x)*unit_step(x-2),5*unit_step(x-2)], [x,-5,5],[y,-10,10])$

p7:wxplot2d([f(x)*unit_step(x-2)], [x,-5,5],[y,-10,10])$

p8:f(2);

p9:f(t)*unit_step(t-2);

p10:p9*exp(0.3*2)*exp(-0.3*2);

p11:laplace(p10, t, s);

p12:part(p11,1);

laplace transfom from  'p12',height =2.744  in 'p7'

p13:part(p12,1);
p14:exp(part(p12,2,2,2));
p15:float(p13*p14)/10;
p16:exp(part(p12,2,2,1));
p17:float(part(p11,2)/10);
p18:(p15/p17)*p16;

result : L{5*exp(-0.3*t)*unit_step(t-2)} = (2.744058180470132*%e^(-2*s))/(s+3/10)

p19:radcan(part(p11,2)/10.0);
p20:part(p19,1,1)/10+part(p19,1,2)/10;

p21:p15/p20*p16;