Swinburne University of Technology
Faculty of Engineering and Industrial Sciences
Mathematics Discipline
Tutorial 2: Half range Fourier series
1.
Classify each of the following functions according as they are even, odd or
neither.
(i)
4
Period
,
2
0
,
4
0
2

,
4
)
(
=
<
<
<
<
−
=
x
x
x
f
(ii)
.
2
Period
,
2
,
0
0
,
cos
)
(
π
π
π
π
=
<
<
<
<
=
x
x
x
x
f
(ii)
.
2
Period
,
2
0
),
2
(
)
(
=
<
<
−
=
x
x
x
x
f
2.
Consider the periodic function
4
2
,
2
2
0
,
4
)
(
<
<
<
<
=
x
x
x
f
(i)
Find the Fourier series for the above function. Graph the periodic
extension on the interval 12<
x
<12.
(ii)
Find the Fourier sine series for the above function. Graph the
periodic extension on the interval 12<
x
<12.
(iii)
Find the Fourier cosine series for the above function. Graph the
periodic extension on the interval 12<
x
<12.
3.
Consider the periodic function
2
1
,
0
1
0
,
1
)
(
<
<
<
<
=
x
x
x
f
(i)
Find the Fourier sine series for the above function.
Graph the
periodic extension on the interval 6<
x
<6.
(ii)
Find the Fourier cosine series for the above function.
Graph the
periodic extension on the interval 6<
x
<6.
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 Three '09
 tomedwards
 Fourier Series, Periodic function, Leonhard Euler, Fourier sine series

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