Re: [Maxima-discuss] Integrating piecewise defined functions

[Jaime V. <vi...@fe...>]

On 27/11/24 21:56, Eduardo Ochs wrote:
> Hi list,
>
> what is the recommended way to integrate piecewise defined
> functions? I tried this,
>
>   f(x) := if     x<0 then 0
>           elseif x<1 then 1
>           else            0;
>   g(x) := if     x<0 then 0
>           elseif x<1 then x
>           else            0;
>   h(x) := integrate(f(t)*g(x-t), t, -2, +2);
>
> and I couldn't find a way to make Maxima calculate this
> integral...

Hello Eduardo,

If you mean the convolution of f and g:

    h(x) := integrate(f(x)*g(x-t), t, 0, x)

I recommend that you use Laplace transforms and expressions, rather than 
"functions":

f: hstep (x) - hstep (x-1);
g: (hstep (x) - hstep (x-1))*x;
F: laplace (f,x,s);
G: laplace (g,x,s);
H: F*G;
h: pwilt (H,s,x);
plot2d ([f,g,h], [x,-2,2], [legend,"f(x)","g(x)","h(x)"]);

Cumprimentos,

Jaime