Department of Mathematics
University of Toronto
office: DH-3017 (at UTM)
e-mail: remus.radu@utoronto.ca
This is our weekly schedule and it will be updated as we advance in the semester, please check regularly.
| Week | Lectures (Assigned Reading) | Assignments |
| Week 1 9/6 - 9/9 |
1.1, 1.2: Differential Equations: introduction & terminology 1.3, Appx A1: Existence and Uniqueness of solutions; Examples |
HW 1
|
| Week 2 9/10 - 9/16 |
1.4: Separable equations and direction fields 1.5: Method of integrating factors 1.6: Exact equations & examples |
|
| Week 3 9/17 - 9/23 |
1.6: Exact equations and substitution methods 1.4, 2.1: Modelling with 1st order differential equations |
HW 2
|
| Week 4 9/24 - 9/30 |
2.1: Autonomous differential equations & the logistic equation 2.2, 2.3: Equilibrium solutions and stability 2.4: Euler's method & graphical analysis of numerical methods |
|
| Week 5 10/1 - 10/7 |
3.1: Second order linear equations; the characteristic equation 3.1, 3.3: Homogeneous equations with constant coefficients 3.2, 3.3: Higher order differential equations & Examples 3.5: Nonhomogeneous equations, particular solutions |
|
| Week 6 10/8 - 10/14 |
Fall Break |
Practice Problems |
| Week 7 10/15 - 10/21 |
3.5: Nonhomogeneous equations & Examples 3.4, 3.6: Mechanical vibrations; free and forced oscillators |
|
| Week 8 10/22 - 10/28 |
Review | |
| Midterm – Thursday, October 25, in class – Version1 – Version2 | ||
| Week 9 10/29 - 11/4 |
4.1, 5.1: Systems of differential equations 4.2: The method of ellimination & Examples 5.2: The eigenvalue method for homogeneous systems & Examples |
HW 3 |
| Week 10 11/5 - 11/11 |
5.5: Multiple eigenvalue solutions; Generalized eigenvectors 5.5: Algebraic and geometric multiplicities 5.6: Exponential of a matrix and linear systems |
|
| Week 11 11/12 - 11/18 |
5.7: Nonhomogeneous linear systems 5.3, 6.1: Stability analysis of linear and nonlinear systems 6.1, 6.2: Critical points, sinks, saddles, sources & Examples |
HW 4 |
| Week 12 11/19 - 11/25 |
6.3: Ecological models: predators & competitors 8.1: Power series solutions |
|
| Week 13 11/25 - 12/2 |
8.2: Series solutions near an ordinary point 8.3: Series solutions near a regular singular point |
Practice Problems
|
| Week 14 12/3 - 12/4 |
3.8, 9.5: An application of ODEs: the heat equation Final review & examples |
|
| Dec 12 | Final exam – 5-7PM in IB110 the final covers everything! | |