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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Fourier Series 10-31
2
222222
111111
12
123456
p
−+−+−+=
(6)
Example 10. 29
For the function defined by the graph below, find the
half-range FCS. [JNTU 2003 S]
Solution The graph is composed of two line seg-
ments OP and PB in intervals
0, ,
22
pp
p
⎛⎞⎛
⎜⎟⎜
⎝⎠⎝
and
,
respecti
v
el
y
, their slopes being +1 and 1.
Equation of OP : y = x
0,
2
p
⎛⎞
⎜⎟
⎝⎠
Equation of PB : y = (x p)
,
2
p
p
⎛⎞
⎜⎟
⎝⎠
0
y
p
P
BA
y
=
p
2
p
2
x
p p
,
22
So, the function f (x) is defined by
,0
()
,
x
fx
x
p/
pp/ p
<< 2
⎧⎫
=
⎨⎬
−2
<
⎩⎭
x
x<
(1)
The half-range FCS is
0
1
1
() cos
2
n
n
fx a a nx
=
=+
(2)
where
/2
0
00/2
222
() ( )a fxdx xdx xdx
ppp
p
p
ppp
==+−
∫∫∫
Example 10.28
Find the half-range cosine series for f ( x) = x(2 x)
in 0 ...
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Publisher Resources

ISBN: 9781299446557Publisher Website