Define L here L := 4;

IiIl

Define the function over 0 < x < L and zero outside g := x -> piecewise( 1 < x and x < 2, x-1, 2 <= x and x < 3, 3-x, 0);

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Extend to an even function over a period -L < x < L (this step and the next only needed for visualization) h := x -> g(x) + g(-x);

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Extend periodically to two periods each side f:= x-> h(x) + h(x-2*L) + h(x+2*L);

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Set tickmarks for x- and y-axis xmarks := [-8,-4,-2,0,2,4,8]: ymarks := [-1,0,1]: Graph the function plot(f(x), x=-2*L..2*L, tickmarks = [xmarks,ymarks],scaling = constrained, color = red, thickness = 3, title = "y = f(x)", discont = true);

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

N is the max number of terms in partial sum N := 10;

IiM1

a := array(1..N): S := array(1..N): Calculate the coefficients for the Fourier cosine series of f(x) a_0 := (1/L)*int( f(x), x=0..L ): for n from 1 to N do a[n] := 2/L * int(f(x)*cos(n*Pi*x/L),x=0..L); if n = 1 then S[n] := a_0 + a[n] * cos(n*Pi*x/L) else S[n] := S[n-1] + a[n] * cos(n*Pi*x/L) end if; end do: Show result FourierPartialSum:=S[N];

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plot([f(x), S[1]],x = -L..L, tickmarks=[xmarks,ymarks], color = [red, blue], scaling=constrained, thickness = 3, discont = true, legend=["f(x)","S_1(x)"]);

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plot([f(x), S[1], S[2]],x = -L..L, tickmarks=[xmarks,ymarks], color = [red, blue, magenta], scaling=constrained, thickness = 3, discont = true, legend=["f(x)","S_1(x)","S_2(x)"]);

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plot([f(x), S[1], S[2], S[3]],x = -L..L, tickmarks=[xmarks,ymarks], color = [red, blue, magenta, black ], scaling=constrained, thickness = 3, discont = true, legend=["f(x)","S_1(x)","S_2(x)","S_3(x)"]);

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with(plots): A := array(1..N): for n from 1 to N do A[n]:= plot([f(x),S[n]],x = -L..L, tickmarks=[xmarks, ymarks], scaling=constrained, color = [red,blue], thickness = [4,2], discont = true) end do: display(seq(A[i],i=1..N),insequence=true);

Warning, the name changecoords has been redefined

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