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MA 321 Introduction to Numerical Methods
Homework 5
Due: 7/17/09
1. Use a divided-dierence table to show that the following data can be represented by a
polynomial of degree 3:
x 2 1 0 1 2
3
y
1
4 11 16 13 4
Solution : Note the following.
x f [] f [, ] f
MA 321 Introduction to Numerical Methods
Homework 3-Solutions
Due: 6/29/09
1. If a = 0.1 and b = 1.0, how many steps of the bisection method are needed to determine
the root with an error of at most 1 108 .
2
Solution : Note that the bisection theorem giv
MA 321 Introduction to Numerical Methods
Homework 2-Solutions
Due: 6/24/09
1. If x and y are positive real numbers within the range of a 32-bit word-length computer
and if x y is also within the range, what relative error can there be in the machine
compu
MA 321 Introduction to Numerical Methods
Homework 1 Solutions
Due: 6/17/09
1. A real number x is represented approximately by 0.6032, and we are told that the
relative error is at most 0.002. What is x.
Solution : We are told that x is the exact value and
MA 321 Introduction to Numerical Methods
Homework 6 Solutions
Due: 7/21/09
1
1. If we estimate 0 x41 dx by means of a lower sum using the partition P = cfw_0, 1 , 1,
+2
2
what is the result?
Solution : Note that the function is always decreasing on the in
MA 321 Intro to Numerical Methods
Exam 1
Score
50
Name
Solutions
Date: June 30, 2009
/ 50
Please answer all questions completely and show all of your work. Be sure to write neatly so
that your solution may be read as you intended it to be read. Partial cr
MA 321 Intro to Numerical Methods
Exam 2
Score
Name
Date: July 22, 2009
/ 50
Instructions:
1. Be sure to write neatly so that your solution may be read as you intended it to be
read.
2. Partial credit will be awarded.
3. Calculators may be used on the exa
MA 321 Introduction to Numerical Methods
Exam 2 Review
Disclaimer: This worksheet contains some problems that you should work on to prepare for
the second midterm exam. This is in no way a preview of the exam and does not cover all
of the topics that coul
MA 321 Intro to Numerical Methods
Exam 2
Score
50
Name
Solutions
Date: July 22, 2009
/ 50
Instructions:
1. Be sure to write neatly so that your solution may be read as you intended it to be
read.
2. Partial credit will be awarded.
3. Calculators may be us
MA 321 Introduction to Numerical Methods
Exam 1 Review
Disclaimer: This worksheet contains some problems that you should work on to prepare
for the rst midterm exam. This is in no way a preview of the exam and does not cover all
of the topics that could b
MA 321 Intro to Numerical Methods
Exam 1
Score
Name
Date: June 30, 2009
/ 50
Please answer all questions completely and show all of your work. Be sure to write neatly so
that your solution may be read as you intended it to be read. Partial credit will be
MA 321 Introduction to Numerical Methods
Homework 4 - Solutions
Due: 7/8/09
1. Find the Lagrange interpolating polynomial of least degree that interpolates the following table:
x 1
012
y
4 3 5 1
Solution : First, we must nd the cardinal polynomials for th
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MA 321 Introduction to Numerical Methods
Final Exam Review
Disclaimer: This worksheet contains some problems that you should work on to prepare for
the nal exam. This is in no way a preview of the exam and does not cover all of the topics
that could be co