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Sixth laboratory - Fall 2002
Due: Friday, November 29, 2002
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your answers frequently by using the submittor
at the end of the page.
The section of the text most relevant to this lab is
Fourier series convergence
In this section of the lab you will investigate the
convergence of the Fourier series of two functions: a
triangular wave and a square wave. The Java applet
tool below will graph any partial sum sn
of either of these
series. You specify which function and which n
to use, and the intervals for the horizontal and vertical
axes (x and y, then click "Plot function"
to see the graph of sn, or "Plot error"
to see f(x) - sn.
If you click on the graph,
the coordinates of the point where you clicked are shown near the top left
of the graph.
Note that to get accurate results, you'll want to "zoom in" on certain
points by choosing appropriate intervals for x and y.
en(x) = f(x) - sn(x) be the error in the n'th partial sum.
Enter in Question 1 the maximum value of
|e19(x)| for the triangular wave (correct to 2 significant digits).
Enter in Question 2 the maximum value of
s19(x) for the square wave (correct to 3
Enter in Question 3 some n for which
|en(x)| < 0.01 for all x for the
triangular wave. Your answer must be within 20% of the least such n.
Enter in Question 4 some n such that for the square wave,
|em(0.1)| < 0.01 for all m > n.
Your answer must be within 20% of the least such n.
Enter in Question 5 the maximum value of sn(x)
for the square wave and the n from Question 4
(correct to 3 significant digits).
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you will not be able to submit your answers from
home, but we cannot guarantee success.
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