Math/CS 466/666
466/666 NUMERICAL METHODS I (3+0) 3 credits
Instructor Course Section Time Room

Eric Olson Math/CS 466/666 Numerical Methods I TR 4:305:45pm DMSC106
Course Information
 Instructor:
 Eric Olson
 email:
 ejolson at unr dot edu
 Office:
 Tuesday and Thursday at 3pm in DMS 238 and by appointment.
 Homepage:
 http://fractal.math.unr.edu/~ejolson/466/
 Assistant:
 Jordan Blocher
 Jordan's email:
 jordanblocher at gmail dot com
 Required Texts:
 Richard Burden, Douglas Faires and Annette Burden,
Numerical Analysis, 10th Edition, Cengage Learning, 2015.
 Supplemental Texts on Numerical Methods:
 Justin Solomon, Numerical Algorithms: Methods for Computer
Vision, Machine Learning and Graphics, CRC Press, 2015.
 David Kincaid and Ward Cheney,
Numerical Analysis: Mathematics of Scientific Computing,
3rd Revised Edition,
Pure and Applied Undergraduate Texts,
American Mathematical Society, 2002.
 Joe Hoffman and Steven Frankel, Numerical Methods for
Engineers and Scientists, Second Edition, CRC Press, 2001.
 Classic Texts on Numerical Methods:
 Kendall Atkinson, An Introduction to Numerical Analysis,
Second Edition, Wiley, 1989.
 Richard Hamming, Numerical Methods for Scientists and Engineers,
Second Edition, Dover, 1986.
 Eugene Isaacson, Analysis of Numerical Methods, Revised Edition,
Dover Books on Mathematics, 1993.
 Supplemental Texts on Computer Programming:

JTC1/SC22/WG14,
C99
Programming Standard, ISO/IEC, 2007.
 Simon Long, Learn
to Code with C, MagPi, 2017.
 Richard Smedley,
Conquer the Command Line, MagPi, 2016.
 Classic Texts on Computer Programming:
 Brian Kernighan, Dennis Ritchie,
C Programming Language, 2nd Edition,
Prentice Hall, 1988.
 Brian Kernighan, Rob Pike,
Unix Programming Environment,
PreticeHall Software Series, 1984.
Student Learning Outcomes
Upon completion of this course
 Students will be able to implement a numerical method to solve a
nonlinear equation using the bisection method and Newton's method.
 Students will be able to solve linear systems using direct and
iterative methods.
 Students will be able to construct interpolating functions.
Announcements
[17Dec2018] Answers to Programming Project 2
I have made an answer key for
programming project 2 to help figure out your grade.
The final exam is scheduled for
Thursday, December 13 from 4:506:50pm in DMSC 106. It will
cover all topics from the study guides for Quiz 1, Quiz 2,
Written Exam Part I and Computer Exam Part II.
[12Dec2018] Answers to Quiz 2 and Exam Part 2
I have posted my code solutions to Quiz 2
and the Computer Exam Part II to help
you study for the final exam.
[08Dec2018] Answers to Written Exam Part I
I have made an answer key for
the Written Exam Part I to help you study for the final.
[05Dec2018] Answers to Programming Project 1
I have made an answer key for
programming project 1 to help guide your work on project 2.
[30Nov2018] Programming Project 2
Programming Project 2 is now available.
It will be due 4:50pm before the final
December 13 in DMSC 106.
There will be twopart exam similar to the
the final held in class on December 6 and December 11.
On December 11 the openbook opencomputer opennotes
parrt of the exam will be held covering the following items:
[06Dec2018] Written Exam Part I
There will be twopart exam similar to the
the final held in class on December 6 and December 11.
On December 6 the closedbook closedcomputer closednotes
part of the exam will be held
covering the following items:
 Statement of Taylor's theorem including all hypothesis and
an exact form of the remainder term.
 Statement of Newton's method.
 Use of Taylor's theorem to show that Newton's method is
quadratically convergent.
 Explain why the number of correct digits in the approximation
about doubles with each iteration of Newton's method.
 Know how to construct Newton's table of divided differences.
 Know how to read off an interpolating polynomial from a
table of divided differences.
 Use Taylor's theorem to show that (f(x+h)f(xh))/(2h)
approximates f'(x) to O(h^{2}) and
that (f(x+h)2f(x)+f(xh))/h^{2} approximates f''(x) to
O(h^{2}).
Be prepared to analyze similar approximations of derivatives.
 Given an approximation of g(x) denoted by approx(h,x) that
is accurate to O(h^{k}) use Richardson's extrapolation to find an
approximation that is accurate to at least O(h^{k+1}) involving
approx(h,x) and approx(2h,x). Be prepared to find similar
extrapolations, for example, involving approx(h,x) and approx(h/3,x)
and so forth.
 Statement of the RK4 method from memory.
 Consider the row elimination and permutation matrices given by
E_{i,j} =
[ r_{i} ← r_{i} − α r_{j}
] and P_{i,j} = [ r_{i} ↔ r_{j} ]
Find i, j, k and l such that
E_{3,2} P_{1,2} = P_{i,j} E_{k,l}.
There will also be
a surprise extracredit problem covering material from the lectures
and the homework.
[20Nov2018] Quiz 2
There will be a quiz held in class on November 20 covering the following
items:
[06Nov2018] Programming Project 1
Programming Project 1 is now available.
It will be due November 29.
[01Nov2018] Web Campus
Quiz 1 scores are now available on
Web Campus.
[18Oct2018] Quiz 1
There will be a quiz held in class on October 18 covering the
following items:
 Statement of Taylor's theorem including all hypothesis and
an exact form of the remainder term.
 Statement of Newton's method.
 Use of Taylor's theorem to show that Newton's method is
quadratically convergent.
 Explain why the number of correct digits in the approximation
about doubles with each iteration of Newton's method.
 Know how to construct Newton's table of divided differences.
 Know how to read off an interpolating polynomial from a
table of divided differences.
 Use Taylor's theorem to show that (f(x+h)f(xh))/(2h)
approximates f'(x) to O(h^{2}) and
that (f(x+h)2f(x)+f(xh))/h^{2} approximates f''(x) to
O(h^{2}).
Be prepared to analyze similar approximations of derivatives.
 Given an approximation of g(x) denoted by approx(h,x) that
is accurate to O(h^{k}) use Richardson's extrapolation to find an
approximation that is accurate to at least O(h^{k+1}) involving
approx(h,x) and approx(2h,x). Be prepared to find similar
extrapolations, for example, involving approx(h,x) and approx(h/3,x)
and so forth.
There will also be
a surprise extracredit problem covering material from the lectures
and the homework.
[02Oct2018] Homework 1 Due
Please turn in Homework 1
in class on October 2.
[28Aug2018] Introductory Lecture
The lecture notes for the introductory lecture
are now available online as well as
all the source code examples
used for computing the EulerMascheroni constant
in the handson discussion.
Extra Credit
Problem 1
Theorem 3.3 on page 109 of our book as stated is incorrect.
This means there is a counter example such that the hypotheses of the
theorem hold but for which the conclusion doesn't.
As a hint, a correct statement of the Theorem could be
For extra credit find a counter example to the incorrect version
of the theorem as stated in the text, write a letter to the author
or publisher explaining your counter example and how the theorem
could be modified so it is correct, show me the letter, and then
mail it.
Sample Code
 aug30 Fixed Point Iteration
 sep04 Newton's Method
 sep06 Newton's Method
 sep11 Machine Epsilon
 sep13 Aitken's Acceleration
 sep18 Muller's Method
 sep20 Divided Differences (incomplete)
 sep25 Divided Differences
 sep27 Approximation of First Derivative
 oct02 Approximation of Second Derivative
 oct04 Rounding Error (incomplete)
 oct09 Rounding Error
 oct11 Extrapolation of Riemann Sums
 oct16 Weights for NewtonCotes
 oct18 NewtonCotes Quadrature
 oct25 Orthogonal Polynomials
 nov01 Adaptive Gauss Quadrature
 nov06 Taylor's ODE Integrator
 nov08 Trapezoid and RK2 Integrator
 nov13 RK4 Integrator
 nov15 RK2/4 Adaptive Integrator
 nov27 Gaussian Elimination (incomplete)
 nov29 Gaussian Elimination
 dec04 LU backsubstitution
Homework and Programming Assignments
 Homework 1 (due October 2):
 Chapter 2.2 # 1abcd, 2ab, 26
 Chapter 2.3 # 6abcdef, 8, 30
 Chapter 2.4 # 10
 Chapter 2.5 # 3, 4
 Chapter 2.6 # 4abefh
 Homework 2 (due November 1):
 Chapter 3.4 # 1ac, 2d, 3ac, 4d, 5abc, 11ab
 Programming Project 1 (due November 29)
(answers)
 Programming Project 2 (due at final exam)
(answers)
Grading
2 Quizzes 20 points each
1 Exam 60 points
1 Final Exam 100 points
2 Homework Assignments 20 points each
2 Programming Projects 20 points each
1 Inclass Lab Work 20 points

300 points total
Exams and quizzes will be interpreted according to the following
grading scale:
Grade Minimum Percentage
A 90 %
B 80 %
C 70 %
D 60 %
The instructor reserves the right to give plus or minus grades and
higher grades
than shown on the scale if he believes they are warranted.
Final Exam
The final exam is scheduled for
Thursday, December 13 from 4:506:50pm in DMSC 106.
Equal Opportunity Statement
The Mathematics Department is committed to equal opportunity in
education for all students, including those with documented physical
disabilities or documented learning disabilities. University policy
states that it is the responsibility of students with documented
disabilities to contact instructors during the first week of each
semester to discuss appropriate accommodations to ensure equity in
grading, classroom experiences and outside assignments.
Academic Conduct
Bring your student identification to all exams. Work independently on
all exams and quizzes. Behaviors inappropriate to test taking may
disturb other students and will be considered cheating. Don't talk or
pass notes with other students during an exam. Don't read notes or books
while taking exams given in the classroom. You may work on the
programming assignments in groups of two if desired. Homework may be
discussed freely. If you are unclear as to what constitutes cheating,
please consult with me.
Last Updated:
Tue Aug 28 16:19:03 PDT 2018