Instructor: Dr. Lucy Campbell
Lectures:
Wednesdays and Fridays, 8:30 - 10:00 AM, starting Wednesday January 11.
See the Class Schedule for the classroom location.
Course description:
The course covers qualitative theory and methods for analysing and understanding the behaviour of solutions of systems of first-order ordinary differential equations. Systems of ODEs can be used to model many real-life problems where there is some quantity that changes with time. The time evolution of the system can be represented by a phase portrait. A classic example is the Lorenz system which was proposed as a model for convection in the atmosphere but is also relevant in other contexts such as in physics, chemistry and biology.
Course outline:
Basic concepts of dynamical systems. Vector formulation for systems. Theory of autonomous systems in one, two and higher dimensions. Limit sets, stability. Phase plane, qualitative interpretation, limit cycles and attractors. Parametric dependence, bifurcations and chaos.
References:
Prerequisites:
The prerequisites for this course are MATH 3001 (Real Analysis) and MATH 3008 (Ordinary Differential Equations), or permission of the School, i.e., if you do not have the above-stated prerequisites and you wish to take the course, you need to have my permission before you register for the course.
Grading scheme:
There will be assignments, a midterm in-class exam and an end-of-term formally-scheduled exam.
More information:
If you plan to take this course and want more information, you can send me e-mail at campbell(at)math(dot)carleton(dot)ca.
Academic Accommodation:
You may need special arrangements to meet your academic obligations during the term.
Pregnancy or Religious obligation:
Write to me with any requests for academic accommodation during the first two weeks of class, or as soon as possible after the need for accommodation is known to exist.
Academic accommodations for students with disabilities:
The Paul Menton Centre for Students with Disabilities (PMC) provides
services to students with Learning Disabilities (LD), psychiatric/mental
health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism
Spectrum Disorders (ASD), chronic medical conditions, and impairments in
mobility, hearing, and vision. If you have a disability requiring academic
accommodations in this course, please contact PMC at 613-520-6608 or
pmc@carleton.ca for a formal evaluation. If you are already registered with
the PMC, contact your PMC coordinator to send me your Letter of
Accommodation at the beginning of the term, and no later than two weeks
before the first in-class scheduled test or exam requiring accommodation (if
applicable). After requesting accommodation from PMC, meet with me to ensure
accommodation arrangements are made. Please consult the PMC website for the
deadline to request accommodations for the formally-scheduled exam (if
applicable).