622 Higher Engineering Mathematics
in the range 0 to 2π.
y
0
21
1
2
Figure 67.5
- Sketch the waveform defined by:
f(x)=
⎧
⎪⎪
⎨
⎪⎪
⎩
1 +
2 x
π
, when−π<x< 0
1 −
2 x
π
, when 0<x<π
Determine the Fourier series in this range.⎡
⎢
⎢
⎣
f(x)=
8
π^2
(
cosx+
1
32
cos3x
+
1
52
cos5x+
1
72
cos7x+···
)
⎤
⎥
⎥
⎦
- For the Fourier series of Problem 8, deduce a
series for
π^2
[^8
π^2
8
= 1 +
1
32
+
1
52
+
1
72
+
1
92
+···
]