Remus Radu


Department of Mathematics
University of Toronto


office: DH-3017 (at UTM)
e-mail: remus.radu@utoronto.ca

MAT244H5F: Differential Equations I
Fall 2018
Schedule & Homework

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 classVersion1Version2
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!  
Last updated November 2018