Introduction to Numerical Analysis
Math 104A, Winter 2009
Instructor:
Carlos J. Garc´
ıaCervera
March 17th, 2009
Answer the following 8 questions. Show all your work for full credit. You must
include your computer programs. Follow the guidelines for presentation of results
.
Name:
Due on Tuesday March 17th, before 4pm.
Problem 1:
out of 10.
Problem 2:
out of 20.
Problem 3:
out of 10.
Problem 4:
out of 25.
Problem 5:
out of 20.
Problem 6:
out of 20.
Problem 7:
out of 35.
Problem 8:
out of 40.
Total:
out of 170.
THESE SHEETS ARE TO BE HANDED IN WITH YOUR EXAM.
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View Full DocumentMath 104A
Final Exam
Winter 2009
1. (10 points) An amount of
P
1
dollars is put into an account at the beginning of years 1
,
2
, . . . , N
1
.
It is compounded annually at a rate or
r
(e.g.,
r
= 0
.
05 means a 5 percent rate of interest).
At the beginning of years
N
1
+ 1
, . . . , N
1
+
N
2
, a payment of
P
2
dollars is removed from the
account. After the last payment, the account is exactly zero. The relationship of the variables
is
P
1
±
(1 +
r
)
N
1

1
²
=
P
2
±
1

(1 +
r
)

N
2
²
.
If
N
1
= 30,
N
2
= 20,
P
1
= 2000, and
P
2
= 8000, then what is
r
?
2. (10 points) Consider the following iterative method to solve
f
(
x
) = 0:
x
n
+1
=
g
(
x
n
)
,
where
g
(
x
) =
x

f
(
x
)
f
0
(
x
)

1
2
f
00
(
x
)
f
0
(
x
)
³
f
(
x
)
f
0
(
x
)
´
2
.
(a) (5 points) Does the method converge?
What is the rate of convergence of the method?
Justify your answer.
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 Fall '08
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 Numerical Analysis

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