Instructor Course Time Room
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Eric Olson Math 466/666 Numerical Methods I TR 3:00-4:15pm Remote
David Kincaid and Ward Cheney,
Numerical Analysis: Mathematics of Scientific Computing,
3rd Revised Edition,
Pure and Applied Undergraduate Texts,
American Mathematical Society, 2002.
R.J. Hosking, S. Joe, D.C. Joyce, J.C. Turner,
First Steps in Numerical Analysis, 2nd Edition, Hodder
Education Publishers, 1998.
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.
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.
August 25 -- Course Outline and Section 1.2 Types of Errors
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:
Use the bisection method to search for a
critical value where a system, process or function changes
state or behavior.
Construct an interpolating polynomial
p(x) of degree n-1 passing through the points
(xi,f(xi)) where i=1,...,n
and then evaluate it at a specified value x=α.
Use the Secant Method to approximate
x such that f(x)=0.
Use Aitkin's δ2 process
to accelerate a linearly convergent sequence.
[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:
Definition and computation of the vector p-norms.
Definition of the induced or natural matrix p-norm.
Given a matrix A compute the matrix 1-norm and the ∞-norm.
Definition of absolute, relative error and significant digits.
Given an approximation ξ of the exact value x, be able
to compute the absolute and relative error in ξ.
How to contruct the Lagrange interpolating polynomial of
degree n−1 passing
through specified points for
(xi,yi) for i=1,...,n.
Exact statement of the theorem on the error in interpolating
polynomials (see the end of the lecture notes from September 8 and
also Homework Assignment 1).
Definitions of the difference operators E, Δ, ∇ and δ.
Statement of Newton's binomial theorem.
If f(x) is a polynomial of degree n, be able to prove that
Δnfj and
∇nfj are constants.
[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
Commentary with mathematical notation.
Functioning Julia code.
Scanned-in pencil-and-paper work.
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
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
https://unr.zoom.us.
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.
Grading
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
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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.
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 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.
Netiquette
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.
Diversity
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.
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
