MAT267, Fall 2007


Math 267 - Fall 2007
Faculty: Vitali Kapovitch Office: ES 2146 Telephone: (416)-978-6786 email: vtk@math.toronto.edu Office Hours : M 3-4pm, F 11-12 and by appointment "He who asks is a fool for five minutes, but he who does not ask remains a fool forever". -- Chinese Proverb	Teaching Assistant : Tim Tzaneteas Office: BA 6135 Telephone: 416-978-4794 email: ttzanete@math.toronto.edu


General Info

The Texts for this course: Lecture Notes + "Differential equations, dynamical systems, and an introduction to chaos" by Hirsch, Smale and Devaney,

Sections 1.1-1.2, 2.1-2.7, 3.1-3.4, 4.1-4.3, 5.1-5.5(review), 6.1-6.4, 17.1-17.6, 8.1-8.5, 9.1-9.4, 10.1-10.3, 10.5+ lecture notes

Homework- 25%
Term Test - 30%
Final Exam - 45%

Extra credit - 3%

The course letter grade will be calculated as follows

Homework assignments will be posted every Tuesday after the lecture. It will be due the following Tuesday at the lecture.
NO late homework will be accepted.
Extra credit can be earned by submitting solutions to extra credit homework problems and by spotting mistakes during lectures
Important: There will be no make up midterms! If you have a valid reason to miss the term test, the corresponding portion of the Final exam will count as your term test grade.

Announcements

I will have extra office hours on Wednesday, December 12, from 5-6pm.
Here are the solutions to the practice final.
The final exam will cover all the material covered in lectures and homework. The material from the book which was not covered in class will NOT be on the exam. Specifically, the exam will cover the following topics:

Material from the lecture notes: Separable equations, 1st and second order linear equations, exact equations, variation of parameter, linearity principle.
Material from the book:

Planar linear systems: Sections 2.1-2.7;
Phase portraits of planar systems: Sections 3.1-3.4;
Trace-determinant plane: Section 4.1;
Real canonical form: Section 5.5
Higher dimensional linear systems: Sections 6.1,6.3, 6.4 (matrix exponential), 6.5 (variation of parameter);
Nonlinear systems: Sections 17.1-17.2(existence and uniqueness) 17.3 (continuous dependence on initial conditions and parameter), 17.4( extending solutions);
Equilibria and Stability: Sections 8.1,8.2, 8.4, 9.2, 9.3, 9.4
Anything else we've covered in class but I might have forgotten to mention above.

Here is the final exam from mat267 class I taught last semester.
Here are the solutions to the extra credit problem from homework 7.
Here is a video of the Takoma bridge disaster demonstrating the resonance phenomena.

Exams

Term Test

Final Exam


Homework Assignments