Higher Engineering Mathematics

(Greg DeLong) #1

668 FOURIER SERIES



  1. 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

cos 3x

+

1
52

cos 5x+

1
72

cos 7x+···

)






  1. 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

+···

]
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