Math 234: Differential Equations
New!
Lecture notes for February 24 - 27 are posted
here .
There may be some misprints here and there. Please let me know
if you find any.
About the Mid Term Exam:
The Test will cover linear equations and linear systems of first-order and
higher order. This will include:
* all of chapter 3 of the textbook
* first-order linear systems, including the material covered in the
handout
http://www.math.toronto.edu/rjerrard/234/systems.pdf
(up through the end of Section 4.1) and covered on the homework assignment
http://www.math.toronto.edu/rjerrard/234/assignment1.pdf.
Material from the last part of the above notes (Section 4.2 and later),
as well as from this week's lectures,
will NOT be covered until some later quiz or test.
* in principle there might be material on first-order linear equations
from chapter 2 (eg, section 2.1). It is helpful to review this in any
case, if you have time, to see the how it relates to the second-order
equations and first-order systems that we have discussed more recently.
Instructors
| Lecturers |
contact information |
office hours |
Robert Jerrard
LEC 01 | 3145 ES
|
Monday 4-5pm |
Wolfgang Staubach
LEC 02 | 4051 SS
wolf@math.utoronto.ca
(416) 978-3484
|
TBA |
Text
Boye and DiPrima,
Elementary Differential Equations and Boundary Value Problems,
seventh edition. Any version of the seventh edition is okay --- you are not
required to get the ``Course Advantage Edition''.
Marking Scheme.
Marks will be based on
Terms Tests, one Midterm Exam, and
a Final Exam.
Policies regarding the use of calculators and aid sheets on exams will be
announced within a couple of weeks.
The marking scheme is summarized in the following table.
| what |
tentative time |
percentage of final course mark |
| Term Test 1 | Tuesday February 4, 3-4:30pm |
15% |
| Mid Term Exam | Tuesday, March 11, 3-5pm |
30% |
| Term Test 2 | Tuesday March 25, 3-4:30pm |
15% |
| Final Exam | to be announced |
40% |
Homework
Problem sets and related information will be posted online.
Problems will not be marked, but solutions will be posted online,
and if there are problems that you do not understand, you should
check them against the online solutions.
Doing the homework promptly is essential to learning the
material.
Tutorials
Tutorials will take place according to the following schedule:
| Tutorial |
when and where |
| TUT 1/01 |
Tuesdays 3-4:30pm, SF3201
|
| TUT 1/02 |
Tuesdays 3-4:30pm, SF3202
|
starting on January 14. The tutorial time slot will be used for
the Term Tests and perhaps also for the Midterm Exam.
Course Outline
Topics will include
- First order ODEs (Chapter 2 of the textbook)
- linear equations
- separable equations
- autonomous equations
- exact equations
- some applications
- linear equations of higher order (Chapters 3 and 4 of textbook)
- homogeneous 2nd order equations
- nonhomogeneous 2nd order equations
method of undetermined coefficients, variation of parameters
- applications
- higher-order equations
- first-order systems of linear equations (Chapter 7 of the textbook
and handouts of lecture notes)
- review of matrices; matrix exponentials
- solution of first-order systems with constant coefficients
- Laplace transform (Chapter 6 of the textbook)
- Definition and basic propoerties
- Laplace transform of derivatives, inverse Laplace transform
- Solving ODEs using Laplace transform
- Partial differential equations (Chapter 10 of the textbook)
- The concept of partial differential equations
- some facts about fourier series
- The method of separation of variables
- the heat equation and wave equation
- Laplace's equation