APPM 4/5350 Worksheet Week 6
Figure 1:
www.xkcd.com
1.
Integration
If you were to find and Integrate the Fourier Cosine Series of the function in part
(
a
)
would you get the
Fourier sine series of part
(
b
)
? Explain why or why not.
(a)
h
(
x
) =
x
0
< x < L
(b)
k
(
x
) =
x
2
2
0
< x < L
2.
Complex Fourier Series
Find the Complex Fourier Series for
g
(
x
) =
x

L < x <
1
1
1
< x < L
Write an expression relating the normal Fourier coeffecients
a
n
and
b
n
to the complex Fourier coeffient
c
n
.
(Hint: rewrite the expression
f
(
x
) =
a
0
+
∞
X
n
=1
(
a
n
cos(
nx
) +
b
n
sin(
nx
))
in terms of complex exponentials.)
3.
Whats in a Name
What does the name Gibbs have to do with Fourier Series (draw a picture)
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 Fall '08
 ABLOWITZ
 Fourier Series, Leonhard Euler, complex Fourier series, Anil Damle

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