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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
Interpolation 6-5
E moves forward a value f
x
to the next higher
value f
x+h
. Applying E again
E
2
f
x
= E(Ef
x
) = Ef
x+h
= f
x+2h
(6.29)
In general
1
1
()
nn
xx
xn
h
Ef EE f Ef
+−
==
(6.30)
We also define the inverse operator E
1
by E
1
f
x
= f
xh
, so that E
2
f
x
= f
x2h
, etc.
The Identity Operator 1
We introduce a fourth operator 1 called the identity
operator, which is defined by
1f
x
= f
x
(6.31)
6.3.3 The Relations Between
D, , E and 1
Since
D f
x
= f
x+h
f
x
= E. f
x
1. f
x
or
Ef
x
= 1f
x
+ D f
x
= (1 + D)f
x
(6.32)
Thus, E and 1 + D when applied on a function f
x
produce the same result. Hence, they may be treated
as equivalent operators:
E = 1 + D (6.33)
Note ...
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Publisher Resources

ISBN: 9781299446557Publisher Website