Skip to Main Content
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 10-19
b
b +2
p
a
a +2I
z
x
If we change the interval from (b, b + 2p) of length
2p to an interval (a, a + 2l) of length 2l then we
have to substitute
22
,
zx
l
x
zdzdx
ll
p
pp
==
⇒==
variable
length of the interval
(10.29)
Also,
z = b x =
l
p
b = a (say)
z = b + 2p
x
l
p
(b + 2p) =
l
p
β
+ 2l = a + 2l
Now, the Fourier series of F ( z) = F
(
)
xlp
=
f (x) (say) is given b
y
0
11
() cos sin
2
nn
nn
a
nx nx
fx a b
ll
pp
∞∞
==
=+ +
∑∑
(10.30)
where the Fourier coeffi cients a
0
, a
n
and b
n
are given
by Euler’s formulas
+
⎛⎞
=
⎜⎟
⎝⎠
2
0
1
(, , ) ()1,cos ,sin
l
nn
nx nx
aab fx dx
lll
a
a
pp
(10.31)
Note 1 Putting x = 0 in (10.31) we have formu-
las for f (x) defined in (0, 2l) and putting ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Mathematical Methods by Pearson

Applied Mathematical Methods by Pearson

Bhaskar Dasgupta
Mathematical Modelling

Mathematical Modelling

Pramod Belkhode, Prashant Maheshwary, Kanchan Borkar, J.P. Modak

Publisher Resources

ISBN: 9781299446557Publisher Website