Math 467/667

Spring 2020 University of Nevada Reno

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

Instructor  Course Section                       Time            Room
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

Eric Olson
ejolson at unr dot edu
Please correspond using WebCampus if possible, if not then put the number 467 in the subject line.
Tuesday and Wednesday at 2:30pm in DMS 238 and by appointment.

Required Texts:

R.W. Hamming, Numerical Methods for Scientists and Engineers, Second Edition (online).

Supplemental Texts on Numerical Methods:

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.

Information about Other Software:

Thomas Williams, Colin Kelley, Gnuplot 5.2: An Interactive Plotting Program, official documentation.

The Julia Project, The Julia 1.2 Language, official documentation.

Student Learning Outcomes

Upon completion of this course, students will be able to:
  1. Use Taylor and Runge-Kutta methods to solve IVP's for ODE's.

  2. Use the shooting and finite difference methods to solve BVP's for ODE's.

  3. Use Numerical techniques to solve elliptic, parabolic and hyperbolic PDE's.

Sample Code and Screenshots


[14-May-2020] Take Home Solutions

My solutions to the take home final is now available. If you see any errors, please let me know.

[13-May-2020] Take Home Final

The take-home part of the final exam is now available here and due Wednesday May 13. Please upload your answers to appropriate places on WebCampus.

[11-May-2020] In-class Final

The in-class part of the final exam is scheduled for Monday, May 11 from 9:50-11:50am on Zoom please see the meeting link in WebCampus.

[10-May-2020] Solution to Homework 1

My solution to Homework 1 is now available. If you see any errors, please let me know.

[09-May-2020] Solution to Project 2

My solution to Project 2 is now available. If you see any errors, please let me know.

[09-May-2020] Homework 1

Homework 1 is available here. Due date will be Saturday May 9 uploaded to WebCampus. Please let me know if you find any errors in the assignment.

[07-May-2020] Thank You

[06-May-2020] Study Guide

The "in-class" part of the final exam will cover the contents of the following lecture notes: 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

  1. Definition of the discrete Fourier transform.

  2. Proof of the discrete Fourier inversion theorem.

  3. Derivation of fast Fourier transform algorithm.

  4. Proof the FFT of length N = 2n takes N log2(N) operations.

  5. Proof of the convergence of Euler's method as h → 0.

  6. Construction of the Gauss quadrature rule.

  7. Proof on the accuracy of Gauss quadrature.
For extra credit and graduate students 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):
  1. Given an inner product, construct orthogonal polynomials with respect to that inner product.

  2. 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.

  3. Given a specified weighted Gaussian quadrature rule for the interval [-1,1] with weight w(x) use it to approximate the integral ∫ab f(x)w(x) dx.

  4. Approximate a solution to the ordinary differential equation initial value problem

    y' = f(t,y),     y(t0)=y0

    for given f, t0 and y0 using a specified Runge-Kutta or Taylor method.

  5. Given a numerical scheme for an ordinary differential equation, compute and draw a graph of the Linear stability domain of that method.

  6. Given a numerical scheme for an ordinary differential equation, determine the truncation error and the resulting order of the method.

  7. Compute the fast Fourier transform of a specified vector whose length is 2n 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.

[08-Mar-2020] The Fast Fourier Transform

I have made lecture notes on the the fast Fourier transform to supplement our text.

[24-Mar-2020] Free Student Maple Promotion

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 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.

[11-Mar-2020] Convergence of Euler's Method

I have made lecture notes on the convergence of Euler's method to supplement our text.

[01-Mar-2020] Project 1

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:
  1. The dot product between two functions.
  2. Gram-Schmidt orthogonalization in function spaces.
  3. Construction of the Gauss quadrature rule.
  4. Proof on the accuracy of Gauss quadrature.
  5. Definition of composite quadrature.
  6. Lemma 2: Bounds estimate for quadrature rules.
  7. Theorem 3: Order of convergence of composite quadrature.
  8. Remark on convergence as collocation points increases.
  9. 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.

[3-Feb-2020] Composite Quadratue

I have made lecture notes on composite quadrature to supplement our text.

[22-Jan-2020] Introductory Lecture

I have made lecture notes on Gauss Quadrature to help people who miss the first lecture catch up.


     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
                              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