courses

MAT244F Ordinary Differential Equations (Fall 2012)

Lectures:

Section L0101: MTR10 RW 110 (Ramsey Wright: 25 Harbord St)
- Professor E. Meinrenken
- e-mail: mein at math.toronto.edu
- office: BA 6112
- office hours: T 1-2 and by appointments

Section L5101: W 6-9 LM 162 (Lash Miller: 80 St. George)
- T. Bazett
- e-mail: trefor.bazett at utoronto.ca
- office: HU 936
- office hours: T 4:30-6:30 BA 6283

Note: You may go to the office hour of either instructor, not only that of your own section. Note that the teaching assistants are holding office hours as well.

Teaching assistants:

Alexander Mc Leod.
Email: amacleod at math.utoronto.ca
Office hours: R 3-4, F 3-4, Lounge of 10th floor at 215 Huron. (Take elevator to 9th floor + one flight of stairs.)
Kyle Thompson.
Email: k3thomps at math.utoronto.ca
Office hours: M 3-4 BA 6180, T 12-1 BA 6283

On Monday, Oct 22 Kyle Thompson's office hours on Monday are at 1-2, BA 6180.

Marking scheme:

There will be three quizzes, two midterms and final exam. The dates for the midterms are

Midterm #1 -- Oct 10
Midterm #2 -- Nov 7

For further information, including the chapters covered on the midterms, click here.

The quizzes take place during class. The dates are as follows:

L0101 (Meinrenken): Sep 25, Oct 25, Nov 22
L5101 (Bazett): Sep 26, Oct 24, Nov 21

For further information, including the chapters covered on the quizzes, click here.

The date/time for the final exam will be announced later.

The term mark will calculated with the following weights: midterm 1 =40%, midterm 2=40%, quizzes=20%. The course mark is calculated as either 60% final exam mark + 40% term mark, or 60% term mark + 40% final exam mark, whichever gives the better result.

Policy for the term tests, quizzes and final exam: No tools or unauthorized aids are allowed. (This includes cell phones, calculators, and other electronic gadgets.) There will be no makeup quizzes or tests. For excused absences (e.g. doctor's note), the missed work is prorated based on the remaining term work.

Please familiarize yourself with the University policy regarding academic integrity.

Textbook:

William Boyce, Richard DiPrima: Elementary Differential equations and Boundary Value Problems (9th edition), Wiley
or
William Boyce, Richard DiPrima: Elementary Differential equations (9th edition), Wiley

Course Outline:

Introduction (1.1, 1.2)
- Types of differential equations (1.3)
- Direction fields for first order ODE's, isoclines (1.1 + extra material)
First order ODE's
- Separable ODE's (2.2)
- Linear first order ODE's: Integrating factor (2.1)
- Exact first order ODE's (2.6)
- Existence and uniqueness theorem for first order ODE's (2.4)
- Autonomous equations (2.5)
- Applications, modeling (2.3, 2.5)
Second order linear ODE's
- Existence and uniqueness theorem (3.2)
- Wronskians (3.2)
- Constant coefficient second order ODE's (3.1)
- Complex roots (3.3)
- Repeated roots, reduction of order (3.4)
- Inhomogeneous equations: Undetermined coefficients, variation of parameters (3.5, 3.6)
- Applications: Oscillations, vibrations (3.7, 3.8)
Higher order linear ODE's
- Existence and uniqueness (4.1)
- Fundamental systems of solutions, Wronskians (4.1)
- Constant coefficient ODE's (4.2)
- Inhomogeneous equations: Undetermined coefficients, variation of parameters (4.3, 4.4)
Systems of first order ODE's
- Relation with higher order ODE's (7.1)
- Review of some linear algebra (7.2, 7.3)
- Existence and uniqueness (7.4)
- Constant coefficient systems (7.5)
- Complex eigenvalues, repeated eigenvalues (7.6, 7.8)
- Fundamental matrices (7.7)
- Inhomogeneous systems (7.9)
Nonlinear Differential Equations and Stability
- Phase portraits (9.1)
- Autonomous systems and stability (9.2)
- Linearizations (9.3)
- Applications (9.4, 9.5)
Series Solutions of Second Order Linear Equations
- Review of power series (5.1)
- Series solution near ordinary point (5.2, 5.3)
- Examples
Review

Important dates:

Oct 8: Thanksgiving
Nov 4: Last day to drop course from academic record and GPA
Nov 12-13: Fall break (no classes)
Dec 4: end of classes
Dec 5: "Make up for Monday classes"

Handouts and additional materials:

Online notes from Paul Dawkins

Direction field plotters from UBC , from Rice
Isoclines applet from MIT ,
Phase lines applet from MIT ,
Damped vibrations applet from MIT ,
Forced vibrations applet from MIT ,
Phase portrait applet from Rutgers ,
Phase portraits for linear 2-by-2 systems: 1, 2, 3,

A physics demonstration of forced vibrations

An example of resonance Another example of resonance

Assignments:

For a list of assigned homework problems, click here. This list will be revised and updated. Do not submit assignments. However, quizzes will contain problems mainly from home assignments.