Fall 2024 - APMA 990 G100

Selected Topics in Applied Mathematics (4)

Introduction to Dynamical Systems

Class Number: 7481

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Oct 11, 2024: Tue, Thu, 10:30 a.m.–12:20 p.m.
    Burnaby

    Oct 16 – Dec 3, 2024: Tue, Thu, 10:30 a.m.–12:20 p.m.
    Burnaby

  • Instructor:

    Razvan Fetecau
    van@sfu.ca
    1 778 782-3335

Description

CALENDAR DESCRIPTION:

Topics vary depending on faculty availability and student interest. Recent offerings include: geophysical fluid dynamics, adaptive numerical methods for differential equations, learning theory, and stability, pattern formation and chaos.

COURSE DETAILS:

The course is a graduate-level introduction to the qualitative theory of ordinary differential equations and dynamical systems.

The course starts with a review of linear ODE systems and of some basic results in ODE theory (existence and uniqueness, smooth dependence on initial conditions, maximal interval of dependence). The course then moves into nonlinear systems and covers general concepts such as phase portraits, stable, unstable and centre manifolds, nonlinear stability and Lyapunov functions, Hartman-Grobman Theorem, periodic orbits and limit cycles, Poincare-Bendixson theory. We will also look into various computational aspects that relate to the theoretical material. Computational explorations of phase portraits, invariant manifolds, limit cycles, etc will be performed using Matlab.

Grading

  • Assignments 50%
  • Final Exam 50%

REQUIREMENTS:

A solid undergraduate-level course in ordinary differential equations (equivalent of SFU's Math 260). A second course in ODE's (equivalent of SFU's Math 467) would be helpful, but it is not required. Basic familiarity with programming in Matlab.

Materials

REQUIRED READING:

"Differential equations and dynamical systems" by Lawrence Perko (Third Edition, Springer-Verlag, 2001).
ISBN: 978-0-387-95116-4

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.