Department of Mathematics

University of Toronto

APM346F. Differential Equations

2000/2001 winter session

Course Information


Cordial greetings

I believe that you are a student taking APM 346 at Winter 2000/2001 session (Fall 2000). Otherwise, why are you wasting your valuable time reading this?

Should you take APM346?

Alternative

There is another course covering PDE (Partial Differential Equations) [with some elements of ODE]: APM351. Differential Equations of Mathematical Physics is supposed to be heavy-duty and more rigorous course designated for mathematicians and those who heavily use PDE (many physicists, some computer science guys (really interested in numerical methods)). If you are going to be one of them and have a good analytical background, you would better take APM351.

Prerequisite

AT235Y/237Y/257Y, 244H. You should be pretty good in Calculus and ODE to excell in this course. Some knowledge of linear algebra (MAT223) and some familiarity with physics would be useful,

Co-requisite

None, but many people taking this course, take MAT334H (Complex Variables) and MAT338 (Introduction to Real Analysis) as well. These two courses overlap slightly with our course and put it on more solid base. While these courses are not `must have' knowledge of complex numbers is assumed.

What's after?

There is not many courses which list our course as prerequisite: APM441H Asymptotic and Perturbation Methods, APM446H Applied Nonlinear Equations and APM466H Mathematical Theory of Finance (this looks weird but in fact is one of many examples of mysterious effectiveness of mathematics: many problems of different origin are mathematically close).

Instructors:

Professor Victor Ivrii

  • Section: L0101.
  • Other duties: course coordinator, markskeeper & webmaster (and the author of this text)
  • Phone: 978-4031
  • e-mail: ivrii@math.toronto.edu
  • Office: SS4057
  • Office hours: TBA; now you can-drop in at any time looking at my schedule

    TA: James Coleman

  • Phone: 978-TBA
  • e-mail: coleman@math.toronto.edu
  • Office: SS 2120
  • Office hours: Wed. 11-12

    Contacting instructors and TA

    To have your mathematical questions answered you can contact any of us. There are some subjets (marks management, make-up) which require to contact course coordinator. Note that no real mathematical consultation will be delivered by e-mail or phone!!!
  • To reach Victor Ivrii you can use e-mail (keeping your messages as short as possible) or phone. You can come in my office as well. You need to look at my time-table to make sure that I am here and you'd better come during my office hours: I will not kick you out if you come in another time but I can be absent or really busy.

  • How to reach James Coleman: The best thing during the office hours; he is not necessary in his office in the other time; you can e-mail or phone him (but his office and phone are shared, so use the phone as the last reserve).

    Textbook and Matherial

    Elementary Applied Partial Differential Equations With Fourier Series and Boundary Value Problems, 3/e by Richard Haberman, Prentice-Hall (1997) 736 pp., ISBN 0-13-263807-X

    We will be covering Chapters 1-12 (completely or partially). We start from the part of Chapter 12 (it is rather easy matherial), and then go in correct order from Chapter 1 to Chapter 11. Some of the sections which seem to be more technical or less important will not be done in depth (or even skipped) but I don't mind if you read them. Chapter 6 (numerical methods) will be surveyed only and to study this topic in depth one needs to take CSC446H Computational Methods for Partial Differential Equations. In general the emphasis in this course will be on solving problems rather than on theory, but problem solving based on a solid grasp of the concepts involved, rather than cookbook recipes. You need to understand approaches rather than remember solutions of the concrete problems.

    An understanding of calculus and ordinary differential equations is essential in this course.

    Evaluation

    There will be 1 MidTerm Test, 2 hours (20%) of the final mark, 3 Graded Home Assigments of the equal weight (10%) of the final mark each , together making 30% of the final mark worth, and Final Exam will be 50% worth. Your final mark will be just a sum of your scores (no belling or bulling). Some of these tests will contain Bonus problems to give you an opportunity to show how smart you are and earn extra points. If your rescaled examination mark will be higher than this sum, you will get the rescaled examination mark. But it doesn't happen often and you should not rely upon this chance!!! Midterm Test (2 hours) will be not in schedule.

    Make-up

    If you missed the test or home work due to really good reasons (from my point of view!) you should contact me as soon as possible (phone and e-mail are OK) and make-up will be arranged if possible. Otherwise, your mark will be rescaled (subject to my discretion). If your case is not so noble or if you failed to contact me promptly (one week after test or dead-line is OK but this period could be extended in some cases) you will get a make-up or rescaling with 10% or 20% reduction of your score for this test (subject to my discretion again). Further, you can make-up up term test you didn't do well with 20% reduction of your second score (you should ask in 7 days after return of the papers). If your first score was higher, it will not be changed. Remember, however, that this is a heavy load for instructor and TA and my intention is to make you to learn more rather than to improve your mark. The grading of term test and home works is done by TA and you should contact him first if you have related questions.

    If you came to course later

    Contact me as soon as possible!

    If you have a problem

    Contact me as soon as possible! Don't let you problem grow-up until it will be mature and hard-to-solve!

    Problem Sets

    The problem sets (usually consisting of problems from the textbook) will be assigned weekly. These problems will be not submitted for marking. Students must do these weekly problems in order to prepare themselves for the GHA, term test and exam. Remember: it is very important to solve all the suggested problems. You can trap yourself frequently applying the rule "I know how to solve this problem, ergo I shouldn't waste the time solving it".

    Quizzes and Graded Home Assignments

    Make-up will be only on the following week. Students, having a good reason to miss the test and make-up should be ready to submit the proof.

    Final Exam

    The procedure is completely determined by University policy. No frills! No early sitting, make-up and you will not get your papers back unless you pay some fee (instructors don't get their fair share; actually they didn't get any share of this fee at all)

    Solutions

    will be provided after the tests shortly (including final exam).

    Marks management

    As soon as your tests are graded I put the marks in the Master-File (or rather bunch of them) in my computer. Further, I put marks for every final exam problem in the Master-File. Note, that only this file is used for the final mark calculation. But errors are possible: TA can make problems grading errors, I have yet to see TA who is proficient in arithmetics and I make typing errors. To find errors you must browse your marks in my office or on-line; further you must get your paper, check TA marking, arithmetics and compare master-file mark with the real one. To correct the error you should bring the paper to my office (to be sure that I make a correction). I can correct TA errors in mark calculation only; for grading discussions you must contact TA. Note, that you should get your paper and check it and browse your mark-on-line!

    Marks-on-line

    You can browse your personal marks via WWW (URL is where yourpass is some special password. By the default, it is your stutent' ID number. If you want a better privacy protection you will get a really hard-to-crack (and hard-to-remember!) yourpass coming to my office. I hope that you will neither give yourpass to anybody nor put it on your home page as one whiz kid did some time ago. Note, that the file you are browsing is not a master-file but it is generated from master-file by some script I run only after major changes of the master-file. So, any correction of your mark in my master-file affects marks-on-line with some delay. Anyway, this file-on-line is not used for any calculation. And again browsing marks doesn't mean that you need not to get and check your real paper: you still must: first, you need to read TA's notes (which can be really useful); second, you can discover marking and copying errors. Further, knowing your score for each final exam problem you can decide if you really want to pay to recover your work. You can see how it looked like one year ago

    M.A.C. at Sidney Smith

    This M.A.C. means Math Aid Centre. It is open during the week, starting the week of October 1. The hours of operation and location will be announced. Any important information concerning the course will be posted on the APM 346 notice board inside the above M.A.C.


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