f:=x->(-1)*(u(x+1)-u(x))+((-1+2*sin(Pi*x))*(u(x)-u(x-1)));

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgtSSJ1R0YlNiMsJjkkIiIiRi9GLyEiIi1GKzYjRi5GLyomLCZGMEYvLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJkkjUGlHRjhGL0YuRi8iIiNGLywmRjFGLy1GKzYjLCZGLkYvRjBGL0YwRi9GL0YlRiVGJQ==

plot(f(x),x=-3..3);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

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

JSFH

We can see that T=2

alias(u=Heaviside);

SSJ1RzYi

f:=x->(-1)*(u(x+1)-u(x))+((-1+2*sin(Pi*x))*(u(x)-u(x-1)));

plot(f(x),x=-3..3);

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

N:=25;T:=2;

IiNE

IiIj

a:=array([],0..N);b:=array([],0..N);

PTYiNiM7IiIhIiNERVxbbCE=

a[0]:=2/T*int(f(x),x=-T/2..T/2);

KiYsJiIiJSIiIkkjUGlHJSpwcm90ZWN0ZWRHISIjRiVGJiEiIg==

for n from 1 to N do a[n]:=2/T*int(f(x)*cos(2*n*Pi*x/T),x=-T/2..T/2); b[n]:=2/T*int(f(x)*sin(2*n*Pi*x/T),x=-T/2..T/2); end do:

n:='n';

SSJuRzYi

F5:=x->a[0]/2+sum(a[n]*cos(2*n*Pi*x/T)+b[n]*sin(2*n*x*Pi/T),n=1..M);

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plot([subs(M=2,F5(x)),subs(M=5,F5(x)),subs(M=25,F5(x))],x=-1..1);

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