Instructor Course Section Time Room
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Eric Olson Math 467/667 Numerical Methods II MW 1:00-2:15pm DMSC106
We are now meeting at the same times through Zoom on the
UNR
WebCampus. Don't forget to continue checking this page as well.
Course Information
Instructor:
Eric Olson
email:
ejolson at unr dot edu
Please correspond using WebCampus if possible, if not then put the number 467 in the subject line.
Office:
Tuesday and Wednesday at 2:30pm in DMS 238 and by appointment.
Arieh Iserles, Numerical Analysis of Differential Equations,
2nd edition, Cambridge Texts in Applied Mathematics.
David Kincaid and Ward Cheney,
Numerical Analysis: Mathematics of Scientific Computing,
3rd Revised Edition,
Pure and Applied Undergraduate Texts,
American Mathematical Society, 2002.
Classic Texts on Computer Programming:
Brian Kernighan, Dennis Ritchie,
C Programming Language,
2nd Edition, Prentice Hall, 1988.
Brian Kernighan, Rob Pike, Unix Programming Environment,
Prentice-Hall Software Series, 1984.
This will be a closed-book closed-notes exam monitored through
Zoom and given during finals week at the scheduled date.
Make sure you have a working web camera or know how to use the
camera on your mobile phone with Zoom by
the exam time at 9:50am on May 11. Please check
WebCampus
for a link to the exact meeting number.
Here is a list of specific topics to help you study. Please know the
Definition of the discrete Fourier transform.
Proof of the discrete Fourier inversion theorem.
Derivation of fast Fourier transform algorithm.
Proof the FFT of length N = 2^{n}
takes N log_{2}(N) operations.
Proof of the convergence of Euler's method as h → 0.
Construction of the Gauss quadrature rule.
Proof on the accuracy of Gauss quadrature.
For extra credit and graduate students
Be able to discuss under what circumstances using a high-order
numerical scheme is important and when it might be better to use a
lower-order scheme with a larger stability domain.
Compare and constrast the advantages and disadvantages of composite
quadrature versus increasing the number of points in a single Gaussian
quadrature to obtain a better approximation.
If you have any questions concerning the exam or any of the above topics
please send me an email or a message using WebCampus.
[02-May-2020] Project 2
Project 2 is now available here.
Due date will be in Saturday May 2 uploaded to WebCampus.
Please let me know if you find any errors in the assignment.
[29-Apr-2020] Computer Quiz Ready
The computer quiz is now ready and available on WebCampus.
As there is a 90 minute time limit, please don't start the
quiz unless you have 90 minutes of uninterrupted time
available. If there are any difficulties with the quiz,
please let me know.
[28-Apr-2020] Computer Quiz Update
As I've had difficulty on two separate occasions--one yesterday and
the other two weeks ago--with my version of Maple sometimes throwing
a licensing error,
I've decided to restrict the computer quiz this week to only
problems that can be worked with Julia.
Therefore, please know how to compute items 3, 4 and 7 from the
list given April 29 below.
For each question on the computer quiz, I will provide a program written
in Julia that is missing some code. Your task for the quiz will be
to fill in the missing lines so the program runs correctly.
[27-Apr-2020] Computer Quiz
We will have our computer quiz sometime next week.
I'm planning to use WebCampus to administer the exam.
Please make sure both Julia and Maple are installed
on your home computer before the exam. In preparation
for the quiz, please know the following topics (but see
the announcement just above where I've restricted the
quiz to items 3, 4 and 7):
Given an inner product, construct orthogonal
polynomials with respect to that inner product.
Given the roots of an polynomial of degree n that is
orthogonal with respect to a specified inner product,
find the weights for the corresponding Gaussian
quadrature formula.
Given a specified weighted Gaussian quadrature rule
for the interval [-1,1] with weight w(x)
use it to approximate the integral
∫_{a}^{b} f(x)w(x) dx.
Approximate a solution to the ordinary differential
equation initial value problem
y' = f(t,y), y(t_{0})=y_{0}
for given f, t_{0} and y_{0} using a specified
Runge-Kutta or Taylor method.
Given a numerical scheme for an ordinary differential
equation, compute and draw a graph of the Linear
stability domain of that method.
Given a numerical scheme for an ordinary differential
equation, determine the truncation error and the
resulting order of the method.
Compute the fast Fourier transform of a specified vector
whose length is 2^{n} for some positive n.
[19-Apr-2020] Solution to Project 1
My solution to Project 1 is
now available. If you
see any errors, please let me know.
[02-Apr-2020] Typo in Project 1
A sign error in the expression for A in problem 1(i) has now been
corrected. Sorry for the mistake.
I have sent each of you a message on WebCampus containing instructions
for obtaining a free version of Maple that can be installed on your home
computer and used for the rest of the course. Please install Maple
and Julia as soon as possible so we don't have to use remote desktop
for our course.
[22-Mar-2020] Mathematica Instead of Maple
Since it may be a few weeks or never before we obtain a Maple
license that is suitable for distance learning, I have
translated
some of our scripts into the Wolfram language.
Note that Mathematica is available through the
UNR
remote desktop.
[21-Mar-2020] Zip Archive of Your Files
Please check your inbox in WebCampus to find a message telling you
how to retrieve a zip archive that contains your files from the
Linux image that we were using in the computer lab.
[23-Mar-2020] Switch to Online Learning
As described at the UNR
webpage on the novel coronavirus
The University will begin online delivery of all for-credit academic
courses Monday, March 23, the week following Spring Break.
The University is directing all students to remain home, not return to
campus, and continue their courses online following the completion of
Spring Break on March 22.
The recommended software for distance learning will be provided by
Zoom Video Communications and accessible by means of a link on our
course page at UNR
WebCampus. Please check the canvas page for the Meeting ID and
Join URL under the Zoom tab.
We will video conference the scheduled classtime at 1:00pm on Monday
and Wednesday. You may need to register for a Zoom account before
then and install the conferencing software on a suitable computer or
mobile phone. Please let me know if you have difficulty installing
the software or finding the Join URL ahead of time so we can fix the
technology before the first class meeting. Given the unique nature
of these arrangements, video attendence will be mandatory.
Project 1 is now available here.
Due date will be Wednesday after Spring Break. Due to the
switch to distance learning, there is an one-week extension
for turning in the programming project. It is now due
anytime during the second week after Spring break and should
be uploaded through WebCampus as Project 1.
[19-Feb-2020] Quiz 1
There will be a quiz covering the lecture notes from
January 22 and February 3 on February 19. Please make sure
you have reviewed the following topics:
The dot product between two functions.
Gram-Schmidt orthogonalization in function spaces.
Construction of the Gauss quadrature rule.
Proof on the accuracy of Gauss quadrature.
Definition of composite quadrature.
Lemma 2: Bounds estimate for quadrature rules.
Theorem 3: Order of convergence of composite quadrature.
Remark on convergence as collocation points increases.
Proof that Gauss quadrature has positive weights.
As per our discussion on Monday topics 2, 3 and 8 are omitted,
topics 1, 4, 5 and 6 are important and topics 7 and 8 are extra
credit and for Math 667.
Written Quiz 1 20 points
Computer Quiz 2 40 points
1 Homework Assignments 20 points
2 Programming Projects 30 points each
In-class Lab Work 20 points
Final Exam (take home) 70 points
Final Exam (in class) 70 points
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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
Monday, May 11 from 9:50-11:50am on Zoom
please see the meeting link in
WebCampus.
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:
Wed Jan 22 12:45:44 PST 2020