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Homework 11
Math 371, Fall 2012
Assigned:
Friday, December 2, 2011
Due:
Tuesday, December 13, 2011
•
Clearly label all plots using
title
,
xlabel
,
ylabel
,
legend
•
Use the
subplot
command to compare multiple plots
•
Include printouts of all Matlab code, labeled with your name, date, and section.
•
Add 12 for page numbers in the international edition.
(1)
(Richardson Extrapolation)
P. 454 #11
(2)
(Newton–Cotes).
Suppose that
f
is a function with four continuous derivatives on the
interval [
a,b
]. Recall that the error bound for the composite trapezoidal rule
T
(
h
) with
panel width
h
is
T
(
h
)

ˆ
b
a
f
(
x
)
dx
=
(
b

a
)
h
2
12
f
Í
(
ξ
)
for some
ξ
∈
[
a,b
]. The error in the composite Simpson’s rule
S
(
h
) with panel width
h
is
S
(
h
)

ˆ
b
a
f
(
x
)
dx
=
(
b

a
)
h
4
180
f
(4)
(
ξ
)
for some (diﬀerent)
ξ
∈
[
a,b
].
(a) Let
f
(
x
) =
e

x
sin
x
. For the composite trapezoidal rule and the composite Simpson’s
rule, ﬁnd the number of panels
n
required to integrate
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 Fall '08
 KRASNY
 matlab

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