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
6-42 Diff erential Equations
and when pn= is an integer the general solution is
121 2
() () ( ) ( )
nn n n
y CJ t CY t CJ x CY x
λλ
=+= +
6.2.12 Orthogonality
Defi nition of orthogonality of functions
A set of functions
12
,,ff
defi ned on some interval [,,]Iab= is said
to be ortho
gonal on I with respect to a weight function
() 0wx >
if
() () () 0
b
mn
a
wx f x f xdx=
for mn
The norm
m
f
of
m
f
is defi ned by
2
() ()
b
mm
a
fwxfxdx=
The functions are called orthonormal of I if they are orthogonal
on I and all have norm equal to unity.
For ‘orthogonal w.r.t. w(x) = 1’ we simply say orthogonal
on I. Thus, functions
12
,,ff are orthogonal on some interval I if
() () ...
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