## MAT 244 Introduction to Ordinary Differential Equations

### General:

#### Description

2019-2020 Timetable Description

First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined coefficients, variation of parameters. Solutions by series and integrals. First order linear systems, fundamental matrices. Non-linear equations, phase plane, stability. Applications in life and physical sciences and economics.

• Prerequisite: (MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1; MAT223H1/ MAT240H1
• Corequisite: MAT235Y1/ MAT237Y1/ MAT257Y1
• Exclusion: MAT267H1, MAT212H5, MAT258Y5
• Distribution Requirements: Science
• Breadth Requirements: The Physical and Mathematical Universes (5)

#### Textbook

Textbook

There are two different books ("with Boundary Value Problems" and without them; the second one is simply a shorter version but it costs the same; so, better to buy or to lease the larger one. BVP for ODE are usually addressed in PDE (Partial Differential Equations) class). Also there are different editions available.

We support both editions publishing on Quercus all home assignments; 11th is preferable (cleaner interface for online version), but do not pay premium if you can get 10th. Actually you can use even earlier editions, especially 9th.

#### Coverage

We will cover (in full or partially) chapters 1, 2, 3, 4, 7 and 9:
1. Introduction
2. First-Order Differential Equations
3. Second-Order Linear Differential Equations
4. Higher-Order Linear Differential Equations
5. Series Solutions of Second-Order Linear Equations
6. The Laplace Transform
7. Systems of First-Order Linear Equations
8. Numerical Methods
9. Nonlinear Differential Equations and Stability
10. Partial Differential Equations and Fourier Series
11. Boundary Value Problems and Sturm-Liouville Theory

#### Learning Resources

This class in the previous years (as I taught)

Other Resources

#### Tests and Quizzes

Tests
• Term Test 1: Oct 21, 2019 (110 min long)
• Term Test 2: Nov 18, 2019 (110 min long)
• Main sitting: 20:10—22:00 (EX 100; EX 200; EX 300);
• Early sitting Nov 18, 8:10-10:00 (EX 300);
• Early sitting Nov 18, 12:10-14:00 (EX 300);
• Early sitting Nov 18, 16:10-18:00 -- if needed only.
• Deferred sitting (Nov 25 or Nov 26) TBD.
Quizzes
• We plan to give 7 Quizzes drawn from the Home Assignments, each worth 3 points, worth together 15 points, with 2 worst dropped. They will be offered either on the Lectures, or on Tutorials (the arrangements could differ for different quizzes).
• If we reduce the total number of quizzes to 6, with 2 worst dropped, each will be 3.75 points worth.
• Home assignments are neither submitted nor graded but Quizzes will be drawn from Home assignments which are due, Quizzes are usually weekly or biweekly and are 15—20 min long in class time.
• Some Quizzes will be offered during lectures, some will be offered during tutorials (see details in the Quiz descriptions; all Quizzes are listed in Modules and in Calendar).

### Marking scheme

Your Final Mark will be computed as follows: \begin{gather} \mathsf{FM}= \min\bigl[ \mathsf{Q} + \mathsf{BM}+\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM},\, 100\bigr],\\[3pt] \mathsf{Q} = \mathsf{Q}_1 + \mathsf{Q}_2+\mathsf{Q}_3 + \mathsf{Q}_4 + \mathsf{Q}_5 + \mathsf{Q}_6 + \mathsf{Q}_7 \qquad \text{with 2 worst Quizzes dropped} \end{gather} where $\mathsf{FM}$ and $\mathsf{FE}$ are your Final Mark, and the Final Exams Mark respectively,
• $\mathsf{T}_1$ and $\mathsf{T}_2$ are your Test 1 and Test 2 marks (each of these tests is worth 20 points),
• $\mathsf{Q}_n$ are Quiz marks (each 3 points worth), $n=1,2,\ldots,7$, two worst of them is dropped, so $\mathsf{Q}$ is 15 points worth,
• $\mathsf{BM}$ is the bonus mark calculated as $\mathsf{BM}=\min (\mathsf{B}_{\text{class}}^{\text{Lec}}+\mathsf{B}_{\text{class}}^{\text{Tut}}+\mathsf{B}_{\text{web}},8)$, where
• $\mathsf{B}_{\textsf{class}}^{\text{Lec}}$, $\mathsf{B}_{\textsf{class}}^{\text{Tut}}$ and $\mathsf{B}_{\textsf{web}}$ are the bonus points for the activity in the class (during lectures and tutorials, respectively) and contributions to the forum.
• $\mathsf{FEM}$ is a Final Exam Mark, 45 points worth.
• Bonuses
• Web Bonus $\mathsf{B}_{\textsf{web}}$ is assigned by the Class Coordinator (and the Forum Administrator) Victor Ivrii based on your Forum Activity (details will be on Forum).
• Lecture Bonus $\mathsf{B}_{\textsf{class}}^{\textsf{Lec}}$ is assigned by your Lecture Section Instructor based on you activity during lectures;
• Tutorial Bonus $\mathsf{B}_{\textsf{class}}^{\textsf{Tut}}$ is assigned by your Tutorial Section TA ased on your activity during tutorials (difficult in tutorials of this size).

### Miscellaneous

Emailing
• You need to send your email to the right person. In particular, all emails concerning Missing Tests and Quizzes, Appeals, Permissions, Missing Marks should be sent to the Class Coordinator (not your Section Instructor). Emails, sent to the wrong person usually will be discarded and will be forwarded only in the exceptional cases (why? because it too time consuming to deal with those who do not read Outlines or Announcements)
• Your subject line should include MAT244 and the subject of the email. Do not respond to the unrelated emails (or if you do, change the subject line).
• Email should contain all necessary information, including your Lecture Section and Tutorial Section (if needed) etc.
• Questions of public interest are not for emails; we have a Forum (for mathematical questions) and Discussions on Quercus (for non-mathematical questions).

Missing Tests
• For each Test (Term Test 1 or Term Test 2) there will be a Deferred sitting, one week after the Test. You are eligible for a Deferred sitting, if you submit a Doctor's Note (see below) covering the regular day of the Test.
• If you missed a regular day of the Test (due to a confirmed illness), and cannot take a Deferred test, you need to submit a Doctor's Note for a Deferred sitting as well.
• If you miss the Test, and the Deferred sitting of the Test, and submitted the Doctor's Notes for both of them, your remaining Test Marks (including Final Exam Mark) will be rescaled accordingly:
• If you missed one test,   $\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM}$ will get a factor $85/65$.
• If you missed two tests, $\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM}$ will get a factor $85/45$.

Missing Quizzes
• Please note, that the Quizzes are offered during regular class hours and therefore there will be no remedy if you miss the Quiz due to a conflict with other academic activity: if it takes place during its regular hours, it is your responsibility to ensure no schedule conflicts; if it is out-off-regular-hours activity (like our Tests), it is responsibility of this class instructor to accommodate you (as we do).
• There will be no deferred sitting for Quizzes, but if you missed a Quiz, say Monday or Tuesday, due to the illness, you may (not must) take it with another section later this week (permission of the Class Coordinator is required!)
• $\mathsf{Q}$ will get a factor $15/(15-LQ)$ with $LQ$ the sum of all legitimately missed quizzes minus 2. Which means that if you have Doctor's Notes for 1-2 quizzes, they are not counted (since 2 worst marks are discarded anyway), if you have Doctor's Notes for 3 quizzes, only 1 is counted and so on.

Doctor's Note
• Doctor's Note aka Verification of Student Illness or Injury form covering the day of the missing Test or Quiz is required. You are required to provide it ASAP, during the same or the next week (extensions are granted upon my discretion).
• You may email to the Class Coordinator (not your section instructor!) a scan of this form when you receive it (it is even more convenient than to bring an actual paper), but then you need to be ready to bring me the original, if I request. You should scan this note using either a scanner, or a special scanning software on your smartphone. Smartphone photos of such notes will not be accepted (Why? Photos are of low quality and/or too large).
• Both paper form and email should have all necessary information (f.e. Q2 in section T0101, September 28). I will not respond to your email, but put a corresponding note in the field TT-notes or Q-notes on Quercus.

Final Exam
• Final Exam is administrated by the Faculty of Arts and Science, if you missed it due to the illness, you need to take a deferred exam, and you need to submit this Doctor's Note and talk to the Faculty or College Registrar (not to us).

Crowdmark

Everything (Tests, Final Exam, Quizzes) are graded using Crowdmark. Please read here. It also covers the Lost work/mark issue.

Remarks
• You can go to any instructor during his office hours.
• You may enroll into any section (subject to a space availability) but you need to stick with your choice.
• You cannot just walk into Early or Deferred Sitting of the Test or to Quiz at another section, without registering or getting permission: there may be not enough space or test/quiz papers (rooms are booked and papers are produced based on the registration or permission issued). If you do so, your mark for this test/quiz will be $0$. Exception: if you writing Quiz with T&E services, you are encouraged to write with the section occupying different time slot; then you can attend your section.
• One time permission to write with a different section could be given only by the Class Coordinator and not by your Instructor or TA (Why? Because the Class Coordinator keeps all records and is responsible for ordering booklets from Printshop and giving booklets to different sections, and booklets for different sections are different) and request must be submitted before a deadline (again the Class Coordinator needs to know the number of copies for each section required before ordering--so there is a deadline for each Test or Quiz; the small number of extra copies is ordered but they are for emergencies only; "Sorry I forgot!" is not an emergency).
• There could be situations or circumstances which are not covered by these Outlines or University & Faculty policies. Please talk to the Class Coordinator (email or just talk). Please do it as soon as possible.

All right-pointed triangles (►) are expandable (click on them!) and down-pointed triangles (▼) are collapsable