Math/CS 466/666
Fall 2023 University of Nevada Reno
466/666 NUMERICAL METHODS I (3+0) 3 credits
Instructor Course Section Time Room
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Eric Olson Math 466/666 Numerical Methods I MWF noon-12:50pm DMS106
Course Information
- Instructor:
- Eric Olson
- email:
- Please contact me through WebCampus
- Office:
- MWF 1:00-1:50PM in DMS 238 and through Zoom by appointment
- Homepage:
- http://fractal.math.unr.edu/~ejolson/466/
- Live Stream:
- If you can't come to class due to sickness, quarantine or other reasons,
please join via the Zoom link in
WebCampus.
- Grader:
- to be determined (contact through
WebCampus)
- Course Textbook:
- Hosking,
Joe, Joyce and Turner, First Steps in Numerical Analysis,
2nd Edition, Arnold, 1996.
- Supplemental References:
- Jeffery Leader, Numerical Analysis and Scientific
Computation, Pearson, 2004.
- Lloyd Trefethen, Numerical Linear Algebra, Siam 1997.
- Justin Solomon,
Numerical Algorithms: Methods for Computer
Vision, Machine Learning and Graphics, CRC Press, 2015.
- Endre Suli, David F. Mayers,
An Introduction to Numerical Analysis, 1st Edition,
Cambridge University Press, 2003.
- Anthony Ralston and Philip Rabinowitz, A First Course in Numerical
Analysis, Second Edition, Dover, 1978.
- Richard Hamming, Numerical Methods for Scientists and Engineers,
Second Edition, Dover, 1986.
Class Handouts
Course materials specific for this section of Math 466 are available
by clicking on this link. Details for how to
access these files may be found on our course page in WebCampus.
Information about Software
Student Learning Outcomes
Upon completion of this course, students will be able to
- The effects of rouding error in numerical computation.
- Newton's method, interpolation and numerical Linear Algebra.
- Practical use of the computer to solve numerical problems.
In-Class Computer Labs
Homework
Lecture Notes
Announcements
[20-Dec-2023] Final Exam
The final exam is Wednesday, December 20, 2023 from 12:45-2:45pm in DMS106.
This will be closed book and closed notes similar in format to the
theoretical midterm.
- Review all checkpoint questions from Steps 1-13, 16-23, 26-27, 29-33.
- Review homeworks 1 to 5 and be prepared to perform simple
calculations related to
- Significant digits, relative error, rounding error.
- Propagated error, generated error.
- Bisection, secant and Newton methods.
- Matrix norms ||A||∞ and ||A||1.
- How to create a difference table.
- Use a difference table to find an interpolating polynomial.
- Be able to state Newton's method for solving f(x)=0.
- Know the statement and proof of Taylor's Theorem.
- Know the statement and proof of the polynomial interpolation theorem.
- Know the proof of the rate of convergence of Newton's method.
- State the Gauss-Seidel method for solving Ax=b and explain what
kinds of matrices A are appropriate for using this method.
- State the power method for finding the eigenvalue of largest
magnitude and a corresponding eigenvector.
- The definition of the Lagrange polynomial basis functions.
- The definition of the condition number of a matrix.
- Know how to use the condition number for backward error analysis.
- Know how to prove that the matrix norm
||A||2 = max{ ||Ax||2 : ||x||2 ≤ 1 }
corresponding to the Euclidian norm is given by
||A||2 = max{ λ1/2 :
λ is an eigenvalue of ATA }.
- Given a matrix A find the Householder reflector for the first
step in the QR factorization.
- State Simpson's method for approximating a definite integral.
- Prove the n-point Gauss quadrature method is
exact for polynomials of degree 2n-1.
- Use Taylor series to derive the n-th order Taylor method.
[16-Dec-2023] Homework 5
Homework 5 is now available, see also the
link above. It covers steps 28 through 30 from our text
and will be due December 16.
[08-Nov-2023] Computer Lab 6
Today we will do Computer Lab 6
in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[01-Dec-2022] Computational Midterm
The computational midterm will be December 1. The format will be similar
to the computer labs but with less detail and a choice of which problems
to work. Please review
- Computer labs 1 through 5.
- Homeworks 2 through 4.
The exam will be open book and open notes. You may use the web browser
to access existing online resources but do not send email or other
electronic messages. Do make posts in online forums, chat groups or
similar. Please work individually. What you submit must refect your
individual efforts. It's better to ask if in doubt whether something is
allowed during the exam.
[28-Nov-2023] Homework 4 Solutions
I have posted solutions to Homework 4 to
help you study.
Please check my answers and let me know if your
see anything wrong.
Note there may be multiple correct ways to work a problem,
so your solution may be correct but different than mine.
[18-Nov-2023] Computer Lab 5
Today we will do Computer Lab 5
in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[20-Nov-2023] Homework 4
Homework 4 is now available, see also the
link above. It covers steps 18 through 24 from our text
and will be due on November 20.
[29-Oct-2023] Homework 3 Solutions
I have posted solutions to Homework 3 to
help you study.
Please check my answers and let me know if your
see anything wrong.
Note there may be multiple correct ways to work a problem,
so your solution may be correct but different than mine.
[20-Oct-2023] Computer Lab 4
Today we will do Computer Lab 4
in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[16-Oct-2023] Homework 3
Homework 3 is now available, see also the
link above. It covers steps 11 through 16 (but not 14) from our text
and will be due on October 25.
[3-Oct-2023] Homework 2 Solutions
I have posted solutions to Homework 2 to
help you study for the exam on Wednesday.
Please check my answers and let me know if your
see anything wrong.
Note there may be multiple correct ways to work a problem,
so your solution may be correct but different than mine.
[2-Oct-2023] Summary of Newton's Method
I've made a summary that combines the results
from Friday and Monday concerning when and how fast Newton's method
converges. This should help when studying for the midterm.
[4-Oct-2023] Theoretical Midterm
The theoretical midterm will be given in class on October 4. Here is
a list of ideas to help you review:
- Review all checkpoint questions from Steps 1 to 10.
- Review homework 1 and 2 and be prepared to perform simple
calculations and derivations.
The computer will not be available for this exam.
- Know the proof of Taylor's theorem.
- Be able to state Newton's method, the secant method and
the bisection method.
- Show that Newton's method is quadratically
convergent.
This is a closed-book closed-notes only scientific-calculator-allowed
in-class exam.
Efforts have been made to keep the arithmetic simple. If it turns out
to be complicated, that's either because I made a mistake or you did.
In either case, do the best you can and check your work where possible.
While getting the right answer is nice, this is not an arithmetic test.
It's more important to clearly explain what you did and what you know.
[29-Sep-2023] Computer Lab 3
Today we will do Computer Lab 3 in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[25-Sep-2023] Homework 2
Homework 2 is now available, see also the
link above. It covers steps 6 through 10 from our text and will be
due on October 2.
[24-Sep-2023] Homework 1 Solutions
I have posted solutions to Homework 1 to
help you study.
Please check my answers and let me know if your
see anything wrong.
Note there may be multiple correct ways to work a problem,
so your solution may be correct but different than mine.
[20-Sep-2023] Homework 1 Due
Turn in of Homework 1 has been postponed and
will be due September 20.
[15-Sep-2023] Computer Lab 2
Today we will do Computer Lab 2 in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[08-Sep-2023] Computer Lab 1
Today we will do Computer Lab 1 in class.
The finished files should be uploaded to WebCampus at the end of class.
Please let me know if you have any difficulties uploading your work.
[01-Sep-2023] Homework 1
Homework 1 is now available, see also the
link above. It covers steps 1 through 5 from our text and will be
due on September 20.
[28-Aug-2023] Welcome Fall 2023
I am looking forward to seeing you August 28 starting the first
week of class.
We will also live stream our class meetings at a link available
in WebCampus and maintain an online archive of course materials
including lecture notes, assignments and other announcements.
The live stream is so people unable to attend on a particular
day can stay informed and have an easier time to catch up.
To promote a learning environment where people feel free to
ask questions, no recordings will be made.
Please do not view the live stream from the classroom
as that can cause network lag and audio feedback.
My lecture notes should complement the notes you take in class.
I'd recommend comparing the notes you take with the ones I post
after class along with the relevant sections from the text.
Then use these three sources of information to create a final
version of your notes. In my experience reviewing the lecture
in this way is important. Though tempting with an iPad, one
should not try make the final version of your lecture notes
during class. That takes too much time and omits the comparison
and review steps mentioned above.
We will be using WebCampus to turn in written homework--either
scanned from pencil and paper or prepared digitally using an
iPad or similar device.
There will also be a number of in-class computing labs.
In addition to the computing labs and written homework, there will
be two exams and a final exam. In person attendance
is mandatory for all exams and the final.
Grading
Theoretical Midterm 50 points
Practical Midterm 50 points
Homework 50 points
Computer Labs 50 points
Final 100 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 it is believed they are warranted.
Quiz and Exam Schedule
There will be two midterms one covering your knowledge of the theory
and another covering your ability to use a computer to perform
practical computations. The final exam will test both. In
person attendance is mandatory for all exams and the final.
Aug 28 -- Overview of the Text
Aug 30 -- Step 1 Sources of Error
Sep 01 -- Step 2 Approximation to Numbers
Sep 04 ***Labor Day***
Sep 06 -- Step 3 Error Propagation and Generation
Sep 08 -- Lab 1 Quadratic Equations
Sep 11 -- Step 4 Floating Point Arithmetic
Sep 13 -- Step 5 Approximation to Functions
Sep 15 -- Lab 2 Scientific Visualization
Sep 18 -- Step 6 Nonlinear Algebraic and Transcendental Equations
Sep 20 -- Step 7 The Bisection Method
Sep 21 -- Step 8 Method of False Position
Sep 25 -- Step 9 Method of Simple Iteration
Sep 27 -- Step 10 The Newton-Raphson Iterative Method
Sep 29 -- Lab 3 Newton's Method
Oct 02 -- Step 10 Newton's Method (continued)
Oct 04 -- Theoretical Midterm
Oct 06 -- Step 11 Solution by Elimination
Oct 09 -- Step 12 Errors and Ill-conditioning
Oct 11 -- Step 16 Testing for Ill-conditioning
Oct 13 -- Special Topic: Matrix Norms and Singular Values
Oct 16 -- Step 13 The Gauss-Seidel Iterative Method
Oct 18 -- Step 17 The Power Method
Oct 20 -- Lab 4 The Spectral Norm
Oct 23 -- Step 18 Tables
Oct 25 -- Step 19 Forward, Backwards and Central Differences
Oct 27 ***Nevada Day***
Oct 30 -- Step 20 Polynomials
Nov 01 -- Step 21 Linear and Quadratic Interpolation
Nov 03 -- Step 22 Newton Interpolation Formulae
Nov 06 -- Step 23 Lagrange Interpolation Formula
Nov 08 -- Step 26 Least Squares
Nov 10 ***Veteran's Day***
Nov 13 -- Step 27 Least Squares and Linear Equations
Nov 15 -- Step 29 Finite Differences
Nov 17 -- Lab 5 Polynomial Fitting
Nov 20 -- Step 30 The Trapezoidal Rule
Nov 22 -- Step 31 Simpson's Rule
Nov 24 ***Family Day***
Nov 27 -- Step 32 Gaussian Quadrature
Nov 29 -- Step 32 Gaussian Quadrature (continued)
Dec 01 -- Computer Exam
Dec 04 -- Step 33 Single-Step Methods
Dec 06 -- Step 33 Single-Step Methods (continued)
Dec 08 -- Lab 6 Numerical Integration
Dec 11 -- In-class Review
Dec 13 ***Prep Day***
Dec 20 Final Exam from 12:45-2:45pm
Course Policies
Communications Policy
Lectures and classroom activities will held in person and live streamed
through through Zoom at the scheduled meeting time listed in MyNevada
for this course.
Please check
the WebCampus page for the Meeting ID and Join URL under the Zoom tab
if you are unable to make it to class.
During the epidemic I discovered that Zoom also allowed me to meet
individually with students who are sick or can't come to campus just
to ask a question.
If you wish to set up an appointment for office hours
please send me a message through
WebCampus.
Late Policy
Students must have an approved university excuse to be eligible for a
make-up exam. If you know that you will miss a scheduled exam please
let me know as soon as possible.
Plagiarism
Students are encouraged to work in groups and consult resources outside
of the required textbook when doing the homework for this class. Please
cite any sources you used to complete your work including Wikipedia, other
books, online discussion groups, generative AI such as ChatGPT as well
as personal communications. Note that answers obtained from any source
should be verified and fully understood for homework to have a positive
learning outcome. In all cases your sources need to be cited.
Exams and quizzes, unless otherwise noted, will be closed book, closed
notes and must reflect your own independent work.
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 send electronic messages, talk or pass notes with other
students during a quiz or exam.
Homework may be discussed freely.
When taking a quiz or exam
don't read notes or books unless explicitly permitted.
Sanctions for violations are specified in the
University Academic Standards Policy.
If you are unclear as to what constitutes cheating,
please consult with me.
Statement on Academic Success Services
Your student fees cover usage of the University Math Center, University
Tutoring Center, and University Writing and Speaking Center. These
centers support your classroom learning; it is your responsibility to
take advantage of their services. Keep in mind that seeking help outside
of class is the sign of a responsible and successful student.
Equal Opportunity Statement
The University of Nevada Department of Mathematics and Statistics
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 speak
with the Disability Resource
Center during the first week of each semester to discuss appropriate
accommodations to ensure equity in grading, classroom experiences and
outside assignments.
For assistance with accessibility, or to report an issue,
please use the
Accessibility
Help Form. The form is set up to automatically route your request
to the appropriate office that can best assist you.
Diversity
This course is designed to comply with UNR Core Objective 10.
More information about the core curriculum may be found in the
UNR Catalog
here.
Statement on Audio and Video Recording
Surreptitious or covert video-taping of class or unauthorized audio
recording of class is prohibited by law and by Board of Regents
policy. This class may be videotaped or audio recorded only with the
written permission of the instructor. In order to accommodate students
with disabilities, some students may be given permission to record class
lectures and discussions. Therefore, students should understand that
their comments during class may be recorded.
Final Exam
The final exams will be held in person at the time listed in
the standard schedule of final exams for this section. Namely,
the final exam is Wednesday, December 20, 2023
from 12:45-2:45pm in DMS106.
Last Updated:
Sat Aug 26 10:48:12 AM PDT 2023