Simon Fraser University
Engaging the World

Course Outlines

Fall 2024 - MATH 716 G100

Numerical Analysis II (3)

Class Number: 3872

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2024: Mon, Wed, Fri, 10:30–11:20 a.m.
    Burnaby

    Oct 15, 2024: Tue, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Dec 7, 2024
    Sat, 12:00–3:00 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

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.

COURSE DETAILS:

This course will be a brisk introduction to scientific computing techniques for continuum models (ODE and PDE). Building on MACM 316, we'll look at the mathematical and computational ideas used to build approximate solutions of partial differential equations.

Topics covered (subject to change) could include: Fourier analysis/FFT, time-stepping methods and the method of lines, spatial discretization schemes, SVD/PCA, compressed sensing, model-order reduction, neural networks, back propagation and physics-informed neural networks.

We shall cover select topics from Parts II, III and IV of the textbook. Be prepared to consult other resources (references to be provided as the class progresses).

The class will operate in a somewhat 'flipped' setting (subject to change): students will be given access to pre-recorded lectures to view before class. During class, we'll delve into the details, and also explore computational ideas. Familiarity with Matlab or Python is assumed. Students will use GitHub for their projects.

Grading

  • Homework Assignments (equally weighted) 45%
  • Project 25%
  • Final Exam 30%

NOTES:

This course is cross listed with MACM 416. For graduate students taking MATH 716, there will be additional problems in each homework, and the scope of the project will be more extensive than in MACM 416.

Materials

REQUIRED READING:

'Data-Driven Modeling \& Scientific Computation: Methods for Complex Systems \& Big Data' by Nathan Kutz. Oxford University Press.

Note: Edition 1 is fine, Edition 2 comes out later in the Fall.

RECOMMENDED READING:

'Data-driven science and engineering : machine learning, dynamical systems, and control' Steven L. Brunton, J. Nathan Kutz, Cambridge University Press

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

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:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website 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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.