Fall 2024 - MACM 416 D100

Numerical Analysis II (3)

Class Number: 4030

Delivery Method: In Person

Overview

  • Course Times + Location:

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

  • Prerequisites:

    (MATH 260 or MATH 310) and MACM 316.

Description

CALENDAR DESCRIPTION:

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Quantitative.

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 45%
  • Project 25%
  • Final examination 30%

NOTES:

Note: this is a cross-listed course with MATH 716. Students enrolled in MATH 716 will do additional homework questions and a more extensive project.

Homework:

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 after the presentation.

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting ofmarks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

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.
ISBN: 9780199660346

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.

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.