Fall 2022 - MACM 416 D100

Numerical Analysis II (3)

Class Number: 6295

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 7 – Dec 6, 2022: 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 is about developing numerical methods for Differential Equations (DEs) from first principles. We will strive to understand how and why they work and where they are used. We will first develop various methods for Ordinary DEs (ODEs), before delving into more advanced problems involving Partial DEs (PDEs). Along the way, we will encounter three of the most important families of numerical methods for DEs: finite difference methods, finite element methods and spectral methods. Continuing a theme first introduced in MACM 316, we will see how numerical analysis relies on a rich and diverse collection of mathematical ideas.

A rough outline (subject to change) is as follows:

1. ODEs
Euler’s method, Taylor methods (review)
Runge-Kutta methods
Multistep methods
Stability

2. Elliptic DEs
Finite difference methods
Finite element methods
Spectral methods

3. Time-dependent DEs
Parabolic equations
Hyperbolic equations

Grading

  • Best 4 out of 5 homeworks 40%
  • Best 3 out of 4 quizzes 36%
  • Project 24%

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:

There is no required reading for this course. Lecture notes will be provided after class.

RECOMMENDED READING:

A First Course in the Numerical Analysis of Differential Equations, 2nd Edition, A. Iserles (2009)

Finite Difference Methods for Ordinary and Partial Differential Equations, R. J. LeVeque (2007)

Spectral Methods in MATLAB, L. N. Trefethen (2000)

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