Example 7.02.2 (Fourier Series) for ENGI 9420 Engineering Analysis

ENGI 9420 Example 7.02.2 Graphs of Partial Sums of Fourier Series
of f (x) = 0 on (-p, 0);
f (x) = (p - x) on (0, +p).

> restart:

> f(k,x) := (1 - (-1)^k)*cos(k*x)/(k*k*Pi) + sin(k*x)/k;

f(k,x) := (1-(-1)^k)*cos(k*x)/k^2/Pi+sin(k*x)/k

> s2(x) := Pi/4 + sum(f(k,x),k=1..2);

> plot(s2(x), x=-Pi..Pi, y=-0.5..3.5, colour=blue, thickness=2,
title=`y = S2(x)`);

[Maple Plot]

> s3(x) := Pi/4 + sum(f(k,x),k=1..3);

> plot(s3(x), x=-Pi..Pi, y=-0.5..3.5, colour=blue, thickness=2,
title=`y = S3(x)`);

[Maple Plot]

> s5(x) := Pi/4 + sum(f(k,x),k=1..5);

> plot(s5(x), x=-Pi..Pi, y=-0.5..3.5, colour=blue, thickness=2,
title=`y = S5(x)`);

[Maple Plot]

> s10(x) := Pi/4 + sum(f(k,x),k=1..10):

> plot(s10(x), x=-Pi..Pi, y=-0.5..3.5, colour=blue, thickness=2,
title=`y = S10(x)`);

[Maple Plot]

> s50(x) := Pi/4 + sum(f(k,x),k=1..50):

> plot(s50(x), x=-Pi..Pi, y=-0.5..3.5, colour=blue, thickness=2,
title=`y = S50(x)`);

[Maple Plot]

The Maple worksheet file is available here.