This file (sadly uncommented) shows the use of Maple to evaluate the Fourier integralsfor the triangle wave problem.int(x*sin(Pi*m*x/L)/L,x=0..L/2) assuming m::integer;

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int((1-x/L)*sin(Pi*m*x/L),x=L/2..L) assuming m::integer;

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I1:=int(x*sin(Pi*m*x/L)/L,x=0..L/2) + int((1-x/L)*sin(Pi*m*x/L),x=L/2..L) assuming m::integer;

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im:=simplify(I1);

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simplify(subs(m=1,im));

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sin(Pi*m/2) assuming m::integer;

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B1:=8/(Pi^2);

NiM+SSNCMUc2IiwkKiRJI1BpR0kqcHJvdGVjdGVkR0YpISIjIiIp

B3:=-8/(3*Pi)^2;

NiM+SSNCM0c2IiwkKiRJI1BpR0kqcHJvdGVjdGVkR0YpISIjIyEiKSIiKg==

B5:=8/(5*Pi)^2;

NiM+SSNCNUc2IiwkKiRJI1BpR0kqcHJvdGVjdGVkR0YpISIjIyIiKSIjRA==

app5:=B1*sin(Pi*x)+B3*sin(3*Pi*x)+B5*sin(5*Pi*x);

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plot(app5,x=0..1);

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