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 Integral Transforms 11-11
1
0
2
0
2
{()} () ()sin
2
sin
1
ss
x
FFs fx Fs sxds
s
esxds
s
p
p
==
⇒=
+
(2)
If we replace ‘x’ by ‘a’ we obtain
22
00
22sin
sin
11
a
sxax
esadsdx
sx
pp
==
++
∫∫
(3)
where we have replaced the dummy variable s by x.
Hence
2
0
sin
2
1
a
xax
e
dx
x
p
=
+
(4)
Example 11.12
Find the Fourier sine transform of
/
ax
ex
Solution By definition, the Fourier sine transform
of f (x) is
0
0
{ ( )} { ( )} ( ) sin
() () sin
ss
ax ax
s
Ffx Fs fx sxdx
ee
fx Fs sxdx
xx
−−
==
=⇒ =
(1)
(2)
Differentiating both sides with respect to ‘s
00
22
0
0
22 22
[ ( )] (sin ) cos
(cos sin)
0(.10)
ax
ax
s
ax
de
F s sx dx e sx dx
ds x s
e
asxssx
as
ea
a
as as
∞∞
==
⎡⎤
=−+
⎢⎥
+
⎣⎦
=− + =
++
∫∫
(3)
Integrating ...
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