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Sixth laboratory  Fall 2002
Due: Friday, November 29, 2002
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The section of the text most relevant to this lab is
11.2.
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 s_{n}
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 s_{n}, or "Plot error"
to see f(x)  s_{n}.
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.
Questions
Let
e_{n}(x) = f(x)  s_{n}(x) be the error in the n'th partial sum.

Enter in Question 1 the maximum value of
e_{19}(x) for the triangular wave (correct to 2 significant digits).

Enter in Question 2 the maximum value of
s_{19}(x) for the square wave (correct to 3
significant digits).

Enter in Question 3 some n for which
e_{n}(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,
e_{m}(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 s_{n}(x)
for the square wave and the n from Question 4
(correct to 3 significant digits).
Submission
There is no reason in principle that
you will not be able to submit your answers from
home, but we cannot guarantee success.
If a submission from within the Mathematics Department system
is not successful, tell the TA.
Comment?
Send questions about problems with submitter to
the lab TA
Send mathematical questions about the labs to
the professor in charge of Math 256:
fournier@math.ubc.ca