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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
6-10 Mathematical Methods
2
1
(1)
()
2!
( 1) ( 2) ( 1)
or
!
() (1)
pn n n n
n
n
pp p
nn nn
pp
yxphypy y
pp p p n
y
n
p
Ey E y y y
n
−−
+
=+=+ +
++ +−
++
⎛⎞
==−=
⎜⎟
⎝⎠
f——
(6.50)
This formula is most suited for interpolation at
the end of the table and also for extrapolation to the
right of y
n
.
Example 6.17
Find the cubic polynomial y
x
which takes on the
values
y
0
= 5, y
1
= 1, y
2
= 9, y
3
= 25,
y
4
= 55, y
5
= 105
Use the difference table to calculate y
3.2
.
Solution Constructing the difference table for the
function we have
Putting
00
1
0
2
30
1,
2
2,
3
3, .
xx xx h
xx
pp
hhh
xx h
xx
p
hh
xx xx h
petc
hh
−+−
=⇒= =−
−−
==−
−−−
==−
formula (6.45) can be put in a simpler form as
fD
DD
D
D
=
== ...
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Publisher Resources

ISBN: 9781299446557Publisher Website