Calculating Fourier coefficients in Maple. I am going to use the triangle wave that we did in class as the example.In this exmple I am going to do the job in a strongly Maple-centric way. I start by defining a function torepresent the triangle wave. This uses Maple's piecewise function.NOTE that I have set the domain to [0,1].f:=x->piecewise(x<1/2,2*x,x>=1/2,2*(1-x));

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlR0kqcHJvdGVjdGVkR0YuNiYyOSQjIiIiIiIjLCRGMUY0MUYyRjEsJkY0RjNGMSEiI0YlRiVGJQ==

Then we can plot that.plot(f(x),x=0..1);

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So that looks beautiful.Now we can ask Maple to do the Fourier integral. We don't have to worry about splitting it into severalpieces; Maple already knows about that.A:=n->int(f(x)*sin(n*Pi*x),x=0..1);

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That did not give us a number, instead it gave us a formula. Now we can feed it numbers to getspecific valuesA(1);

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A(2);

NiMiIiE=

A(3);

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And once we get the idea we can tryA(n) assuming n::integer;

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simplify(%);

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So we get exactly what we got in class without all the work that we needed there!