Math 466/666

Fall 2020 University of Nevada Reno

466/666 NUMERICAL METHODS I (3+0) 3 credits

Instructor  Course                             Time            Room
Eric Olson  Math 466/666 Numerical Methods I   TR 3:00-4:15pm  Remote

Course Information

Eric Olson
ejolson at unr dot edu
Through Zoom by appointment.

Required Texts and Equipment

  1. Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, Second Edition, Dover, 1978.
  2. Home computer running Windows, Linux or MacOS and a suitable web camera. Note that it is possible to provision certain mobile phones as web cameras for use on a computer.

Supplemental Texts on Numerical Methods

  1. Justin Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics, CRC Press, 2015.
  2. David Kincaid and Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Revised Edition, Pure and Applied Undergraduate Texts, American Mathematical Society, 2002.
  3. R.J. Hosking, S. Joe, D.C. Joyce, J.C. Turner, First Steps in Numerical Analysis, 2nd Edition, Hodder Education Publishers, 1998.
  4. R.W. Hamming, Numerical Methods for Scientists and Engineers, Second Edition.
  5. Kendall Atkinson, An Introduction to Numerical Analysis, Second Edition, Wiley, 1989.
  6. Eugene Isaacson, Analysis of Numerical Methods, Revised Edition, Dover Books on Mathematics, 1993.

Information about Software

Student Learning Outcomes

Upon completion of this course
  1. Students will be able to implement a numerical method to solve a nonlinear equation using the bisection method and Newton's method.
  2. Students will be able to solve linear systems using direct and iterative methods.
  3. Students will be able to construct interpolating functions.

Lecture Notes

Here are lecture notes from the distance learning classes to help people catch up who may have experienced technical difficulties during the lecture. Attendance is mandatory and will be taken starting with the second week of class. Don't forget to check WebCampus for graded discussions, pending homework assignments, quizzes and the schedule of Zoom lectures.


[20-Dec-2020] Final Exam Solutions

I have made solutions for the final exam in order to help you better understand my grading. The grades will be finished soon. Have a wonderful winter holiday!

[16-Dec-2020] Final Exam

The final exam is scheduled for Wednesday, December 16 from 2:30-4:30pm through alternative remote. Please make sure you have Proctorio installed on your web browser before the final exam.

[15-Dec-2020] Solutions for Homework 2

I have prepared solutions for the homework on the spectral theorem. If you find any errors in these notes please let me know.

[14-Dec-2020] Project 2 Solutions

I have posted my solutions to Project 2 to help understand how I marked your work and for you to use while studying for the upcomming exam.

[09-Dec-2020] Prep Day

This is the study day after the last day of class and before the final exam.

[08-Dec-2020] Sample Final

I have created a sample exam to help you study for the final.

[08-Dec-2020] Homework 2 Due

A scanned pdf consisting of your written answers to Homework Assignment 2 is due on WebCampus by December 8, 2020. Please upload your work sooner if possible. It may be updated multiple times up until the final deadline.

[01-Dec-2020] Midterm Solutions

The midterm is being graded. I have made a solution key for reference.

[25-Nov-2020] Project 2 Due

The final report in pdf format for Programming Project 2 is due on WebCampus by November 25, 2020. Please upload your report sooner if possible. It may be updated multiple times up until the final deadline.

[11-Nov-2020] Solutions for Homework 1

I have prepared solutions for the homework on Chebyshev polynomials. If you find any errors in these notes please let me know.

[10-Nov-2020] Take Home Exam

On November 10 a take home exam will be made available that is due the following week on November 17.

[29-Oct-2020] Computer Quiz 2

Quiz 2 will be held in class over zoom on October 29. This exam will be open book, open web-browser and open notes. Do not send email, text or any other type of message to anyone during the quiz except the instructor. Please make sure your web cameras are working and have your UNR student ID at hand for identity verification. Note that it will not be possible to take this exam without a working web camera. Check your system is working ahead of time and after that don't change any configuration settings until after the exam. You will also need your own pencil and paper.

You must complete two out of three specified computations. For each computation I will provide a program written in Julia that is missing some code. Your task is to fill in the missing lines so the program runs correctly. You could also create a new program of your own using C, Fortran, Matlab, Python or a different language. In preparation for the quiz, I would recommend that you look over all of the programs written this semester to make sure you understand how they work. In particular, please know how to perform the following tasks using a computer:

[25-Oct-2020] Example Problem

I have created an example problem to help you prepare for the computer quiz on October 29.

[17-Oct-2020] Project 1 Solutions

I have posted my solutions to Project 1 to help understand how I marked your work and for you to use while studying for the upcomming quizzes. You may also download my source file to see how I prepared the report using Jupyter.

[06-Oct-2020] Quiz 1 Solutions

Quiz 1 is now graded. Please check on WebCampus that I have totaled the scores and recorded them correctly. I have made a solution key for reference.

[04-Oct-2020] Project 1 Due

The final report in pdf format for Programming Project 1 is due on WebCampus by October 4, 2020. Please upload your report sooner if possible. It may be updated multiple times up until the final deadline.

[27-Sep-2020] Homework 1 Due

A scanned pdf consisting of your written answers to Homework Assignment 1 is due on WebCampus by September 27, 2020. Please upload your work sooner if possible. It may be updated multiple times up until the final deadline.

[24-Sep-2020] Quiz 1

Quiz 1 will be held in class over zoom on September 24. This exam will be closed book and closed notes. Please make sure your web cameras are working and have your UNR student ID at hand for identity verification. Note that it will not be possible to take this exam without a working web camera. Check your system is working ahead of time and after that don't change any configuration settings until after the exam. You will also need your own pencil and paper.

Quiz 1 will cover the following topics and tasks:

[23-Sep-2020] Finite Differences of a Polynomial

In order to help you prepare for Quiz 1 I have summarized the proof at the end of the lecture notes from September 17 on the finite differences of a polynomial.

[22-Sep-2020] Example Problems

Note there was an error in the matrix 1-norm and the matrix ∞-norm in the original posted version of this pdf file. While the mathematical formulas for these norms were correct, the example computations were mislabeled. Please click reload to make sure you have the corrected version. I'm sorry about any confusion this might have caused.

Here are some worked example problems related to the topics on Quiz 1 which will be given Thursday. This quiz will be closed book and closed notes. Don't forget to study the theorems proofs and definitions as well!

[06-Sep-2020] Using JupyterLab

This video shows how to use JupyterLab to create a report that contains

There was an unfortunate typo in the Julia code used to approximate the limit which appears in the video. The line which read n=2&j should have been n=2^j.

Except for getting the wrong answer, this does not affect the subsequent discussion on how to create a pdf version of the notebook for upload into WebCampus. For reference, the corrected files appear below

[03-Sep-2020] Questions and Answers

There were a number of questions asked through chat about Julia and the computer software we will be using in this class. I have summarized my answers here for future reference.

[30-Aug-2020] Installing JupyterLab

JupyterLab provides a notebook interface that makes using Julia easier to use. Here is a video demonstration how to install the JupyterLab notebook interface.

[25-Aug-2020] First Day of Class

We will meet over Zoom at 3:00pm. Please see WebCampus for the meeting link.

[23-Aug-2020] Installing Julia

We will be using the Julia during this course. This software is open source and available for Windows, Macintosh and Linux. Please try to install Julia your home computer and let me know how it goes. My suggestion is to download the installer from the official project site for Julia and then follow your mouse. Here is a video demonstration.

Once people have installed Julia and verified it is working, I'll further describe how to install the JupyterLab notebook interface.

[19-Aug-2020] Zoom for Students

Information on Zoom for Students is available here. If you sign into Zoom ahead of time using your UNR student account at the UNR Zoom website, you can enter the online class lectures directly and bypass the waiting room.

[04-Aug-2020] Zoom

I will be giving online interactive lectures through the Zoom Video Conferencing system integrated into WebCampus. If possible, please install and test this software before the first day of class. Note that the university has sponsored Zoom accounts for every student. Accounts may be activated by visiting You do not need to pay Zoom any money to use this software on your home computer. My understanding is that study rooms may be reserved in Mathewson-IGT Knowledge Center and equipment checked out from the @One Digital Media and Technology Center by students who need a suitable location to attend lectures delivered over Zoom.

[03-Aug-2020] WebCampus

This course will be delivered through the UNR WebCampus a customized version of the Canvas learning managment platform. According to the documentation Canvas supports access from Windows, MacOS and Linux using current and first previous major releases of the Chrome, Firefox, Edge and Safari browsers. If you are having trouble accessing WebCampus from home or on campus, please contact the UNR OIT Helpdesk.

[02-Aug-2020] Julia

Julia is a free open-source software designed at MIT for performing matrix and vector computations similar to Matlab. This language is quickly becoming popular in science, technology, engineering and mathematics because it is easy to use and generally performs faster than Matlab. Click and install versions can be downloaded for Windows, macOS and Linux from the official Julia language website. If you try to download it over summer and encounter difficulties, please let me know.

[31-Jul-2020] Alternative Remote

This course was originally scheduled to be delivered in-person, but has moved to entirely online due to social distancing and capacity limitations. We will be using a combination of Zoom, WebCampus and other Internet resources which will be announced later. Luckly, this course will not include the additional $34 per credit online fee; however, please make sure you have a computer, suitable web camera and the Internet connection needed for online learning. More information is available at the UNR Coronavirus Information for Students webpage.

[25-Jun-2020] Inspirational Video

Here is an inspirational video from the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory discussing the roles scientific computing and numerical methods are likely to play in the future as computers become more powerful.

[16-Jul-2020] HPC and COVID-19

Here is an interview with Dr Kathy Yelick (the link plays only the part of the show that contains the interview) discussing computational techniques, problems and priorities in the analysis of the coronavirus epidemic.


     COVID-19 Training Quiz     5 points
     Written Quiz              30 points
     Computer Quiz             30 points
     Midterm                   50 points
     2 Homework Assignments    20 points each
     2 Programming Projects    30 points each
     In-class Lab Work         20 points
     Final Exam                70 points
                              305 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.

Course Schedule

Aug 24-Aug 28   Sections 1.1-1.3 Error Definitions
                Sections 1.4-1.6 Computer Arithmetic
Aug 31-Sep 04   Section 2.1 Weierstrass Approximation
                Section 2.2 Bisection Method

*** Labor Day Sep 07

Sep 07-Sep 11   Section 3.2 Interpolation Theorem
                Section 1.3 Matrix Norms
                Section 3.5 Divided Differences
Sep 14-Sep 18   Section 2.3 Peano Kernel Theorem
                Section 2.4 Undetermined Coefficients
Sep 21-Sep 25   Section 3.6 Inverse Interpolation
                Section 3.7 Hermite Interpolation

*** Written Quiz covering 1.1 through 3.2 Sep 24

Sep 28-Oct 02   Section 8.1-8.2 Functional Iteration
Oct 05-Oct 09   Section 8.3 The Secant Method
Oct 12-Oct 16   Section 8.4-8.5 Newton's Method
Oct 19-Oct 23   Section 8.6 Multiple Roots
Oct 26-Oct 30   Section 8.7 delta^2 Acceleration
*** Computer Quiz covering 8.1 through 8.7 Oct 29
*** Nevada Day Oct 30

Nov 02-Nov 06   Section 9.1-9.3 Gaussian Elimination
Nov 09-Nov 13   Section 9.6 Jacobi Iteration
                Section 9.7 Successive Overrelaxation

*** Midterm covering 1.1 through 9.7 Nov 10
*** Veteran's Day Nov 11

Nov 16-Nov 20   Section 9.9 Overdetermined Systems
                Section 9.10 The Simplex Method
Nov 23-Nov 27   Section 10.1 Eigenvectors and Eigenvalues

*** Thanksgiving Nov 26
*** Family Day Nov 27

Nov 30-Dec 04   Section 10.2 The Power Method
Dec 07-Dec 08

*** Prep Day Dec 9
*** Final exam Dec 16 from 2:30 to 4:30pm

Course Policies

Communications Policy

Lectures and classroom activities will be held online through Zoom at the scheduled meeting time listed in MyNevada for this course. Please check the canvas page for the Meeting ID and Join URL under the Zoom tab. To promote an open communication through this interactive environment, video attendance will be mandatory and count as participation in your final grade. If you wish to set up an appointment for office hours please send me a message through WebCampus and ask through chat after one of the online lectures.

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. Homework may be turned in late--with a possible deduction of points depending on the circumstances--as long as I have not already graded the assignment. When attending a Zoom lecture for the course, it's always better to be late than never.


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 as well as personal communications. Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work. Please consult the section on academic conduct below for additional information.


A web camera will be required for this course in order to comply with university requirements for identity verification. Bring your student ID to all online quizzes and Zoom lectures as if attending class on campus. At the beginning of each class please send a quick hello through chat and a quick goodbye at the end. This will indicate to me that you are ready and also count towards your attendance and participation score.


This course is designed to comply with but not satisfy the UNR Core Objective 10 requirement on diversity and equity. More information about the core curriculum may be found in the UNR Catalog here.

COVID-19 Policies

Statement on COVID-19 Training Policies

Students must complete and follow all guidelines as stated in the Student COVID-19 Training modules, or any other trainings or directives provided by the University.

Statement on COVID-19 Face Coverings

In response to COVID-19, and in alignment with State of Nevada Governor Executive Orders, Roadmap to Recovery for Nevada plans, Nevada System of Higher Education directives, the University of Nevada President directives, and local, state, and national health official guidelines face coverings are required at all times while on campus, except when alone in a private office. This includes the classroom, laboratory, studio, creative space, or any type of in-person instructional activity, and public spaces. A "face covering" is defined as a covering that fully covers a person's nose and mouth, including without limitation, cloth face mask, surgical mask, towels, scarves, and bandanas (State of Nevada Emergency Directive 024). Students that cannot wear a face covering due to a medical condition or disability, or who are unable to remove a mask without assistance may seek an accommodation through the Disability Resource Center.

Statement on COVID-19 Social Distancing

Face coverings are not a substitute for social distancing. Students shall observe current social distancing guidelines where possible in accordance with the Phase we are in while in the classroom, laboratory, studio, creative space (hereafter referred to as instructional space) setting and in public spaces. Students should avoid congregating around instructional space entrances before or after class sessions. If the instructional space has designated entrance and exit doors students are required to use them. Students should exit the instructional space immediately after the end of instruction to help ensure social distancing and allow for the persons attending the next scheduled class session to enter.

Statement on COVID-19 Disinfecting Your Learning Space

Disinfecting supplies are provided for you to disinfect your learning space. You may also use your own disinfecting supplies.

Contact with Someone Testing Positive for COVID-19

Students must conduct daily health checks in accordance with CDC guidelines. Students testing positive for COVID-19, exhibiting COVID-19 symptoms or who have been in direct contact with someone testing positive for COVID-19 will not be allowed to attend in-person instructional activities and must leave the venue immediately. Students should contact the Student Health Center or their health care provider to receive care and who can provide the latest direction on quarantine and self-isolation. Contact your instructor immediately to make instructional and learning arrangements.

Local, State and Federal COVID-19 Information

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 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 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.

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.

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 over Zoom or in the classroom 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.

Final Exam

The final exam is scheduled for Wednesday, December 16 from 2:30-4:30pm through alternative remote. Please make sure you have a web camera available for the final exam.
Last Updated: Sun Aug 2 20:59:53 PDT 2020