Skip to Main Content
Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
7-22 Diff erential Equations
Integrating now with respect to ‘s’ we obtain
1
22
1
1
1
() tan
When 0, (0) 0 0 tan 0 0
Hence, ( ) tan ( / ).
s
s
s
s
Fs a ds c
as a
sF cc
Fs sa
==+
+
==⇒=+⇒=
=
(7.86)
Example 7.8.20 Find the Fourier cosine transform of
,for01
() 2 , for1 2
0, for 2
xx
fx x x
x
<<
=− <<
>
.
[JNTU2002, 2003S, 2004S]
Solution The Fourier cosine transform of f (x) is given by
0
12
01 2
!
2
0
2
2
1
2
2
{()} () ()cos
cos (2 )cos 0.
sin
cos
sin cos
(2 ) ( 1)
1sin 0
1
(cos cos0)
(0 sin ) (cos2 cos )
2cos cos2 1
cc
Ffx Fs fx sxdx
x sx dx x sx dx dx
sx
sx
x
ss
sx sx
x
ss
s
s
ss
sss
ss
ss
s
==
=+−+
⎡⎤
⎛⎞
=−
⎜⎟
⎢⎥
⎝⎠
⎣⎦
⎡⎤
⎛⎞
+− −−
⎜⎟
⎢⎥
⎝⎠
⎣⎦
⋅−
=+−
−−
+−
−−
=
∫∫
2
Example 7.8.21 Find the Fourier cosine transfor ...
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

Differential Equations

Differential Equations

Marian Mureşan
Engineering Mathematics

Engineering Mathematics

P. Sivaramakrishna Das, C. Vijayakumari

Publisher Resources

ISBN: 9781299487406Publisher Website