Fall 2020 - MATH 716 G100

Numerical Analysis II (3)

Class Number: 2816

Delivery Method: Remote


  • Course Times + Location:

    Mo, We, Fr 3:30 PM – 4:20 PM

  • Exam Times + Location:

    Dec 18, 2020
    3:30 PM – 6:30 PM



The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.


This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

           Initial Value Problems (3 lectures)
Review of Runge Kutta methods, Euler methods and Taylor methods, stability and stiffness.
Linear Multistep methods, Predictor-corrector methods, Systems of ODEs

            Two point boundary value problems (2 lecture)
Initial value methods (shooting), Finite Differences.

Finite difference formulae
Method of lines
Accuracy, stability and convergence
Lax equivalence
The CFL condition
The von Neumann condition

Fourier Analysis and Spectral methods
Fourier transform, Discrete Fourier transform, 
Fourier Differentiation (Galerkin), Fourier Differentiation (Collocation)
PDE with periodic boundary conditions
Polynomial approximation and differentiation
Polynomial spectral methods


  • Homework 30%
  • Project 20%
  • Midterm 15%
  • Final 35%
  • NB:¬†Please be aware your midterm and final examinations will include an online, timed component, during¬†which time I may use online invigilation software.


Note: this is a cross-listed course with MACM 416.
Students in MATH 716 will do extra problems for their homeworks and their examinations.


You will notice that your homework and project grades are worth a substantial proportion of your final grade. It is in your best interest to do your homework carefully. Any programming that you do must be clearly commented. On occasion, you may be required to hand in your programs. While you are encouraged to work in groups, I must be convinced that the work you hand in is your own.  In cases of academic dishonesty, you will receive zero for the work in question, and an academic dishonesty report will be filed.

Course Project:
The course project will consist of a written report, short oral presentation and computed examples on a topic that may not been directly covered in class but is within the scope of this course. Presentations will be in class, the report will be handed in before our presentations.



We shall be following Spectral Methods by L.N. Trefethen (SIAM).
(Students should be able to obtain it from the SIAM website at the student member rate) 

We will extensively be using the MATLAB code associated with the Spectral Methods textbook. The codes are available for free at https://people.maths.ox.ac.uk/trefethen/spectral.html

You will also be required to download and install the free MATLAB toolbox called Chebfun, by L.N. Trefethen. It can be found at www.chebfun.org.


We will also reference Approximation Theory and Approximation Practice by L.N. Trefethen. 

Supplementary suggested reading includes the MACM 316 textbook.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:


SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html


Teaching at SFU in fall 2020 will be conducted primarily through remote methods. There will be in-person course components in a few exceptional cases where this is fundamental to the educational goals of the course. Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment acknowledges that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

Students with hidden or visible disabilities who believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112).