## Department of Mathematics

### General:

#### Description

2018-2019 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:

In comparison with 10th Edition, 11th has an additional author. Usually the main difference between edition is that the problems are shuffled; so their numeration differ. We support both editions (on Quercus); 11th is preferable.

#### 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

Note: Chapter 5 will be covered (if at all) at the very end of the course, if the time permits.

### Learning Resources

#### This class in the previous years

This class in the previous years (as I taught)

• WolframAlpha

• ODE Plotters

### Tests and Quizzes

#### Tests

• Term Test 1 Monday,  October 15,  20:00—22:00 (2 hours long) EX 100, EX 200, (EX 310).
• Term Test 2 Monday, November 19, 20:00—22:00 (2 hours long) EX 100, EX 200, (EX 320).
Notes: Later we will schedule early sittings.

We plan to grade Tests and the Final Exam using Crowdmark. Details will be available later.

#### Quizzes

We plan to give 7 Quizzes, each worth 4 points, worth together 20 points. 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, each will be 5 points worth.

Home assignments are neither submitted nor graded but Quizzes will be drawn from Home assignments which are due, Quizzes are usually biweekly and are 15—20 min long in class time, see Lecture Notes which cover also Home assignments, Quizzes and Handouts.

### 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 4 points worth), $n=1,2,\ldots,7$, two worst of them is dropped, so $\mathsf{Q}$ is 20 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, 40 points worth.

### Miscellaneous

#### Emailing

Your subject line should start from MAT244 and include 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).

#### Missing work

If you missed some Test or Quizzes
• There will be no make up (even) for a legitimately missing work, but the remainder will count heavier. Namely: $\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM}$ will get factor $80/(80-L)$ with $L$ the sum of all legitimately missed tests.
• Similarly $\mathsf{Q}$ will get a factor $20/(20-LQ)$ 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.
• Since there will be early and late sittings for Tests and since Quizzes are during class time you need to provide a Verification of Student Illness or Injury form covering the day of the missing test. You are required to provide it ASAP to the Class Coordinator not your Section Instructor), during the same or the next week (extensions are granted upon Class Coordinator's 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 requested. You should scan this note using either a scanner, or special scanning software on your smartphone. Cellphone photos of such notes will not be accepted.
• Both paper form and email should have all necessary information (f.e. Q2 in section T0101, September 28). Class Coordinator will not respond to your email, but put a corresponding note in the field TT-notes or Q-notes on Quercus.
• Final exam is administrated by the faculty, if you missed it due to the illness, you need to take a deferred exam, and you need to submit this form and talk to the Faculty or College Registrar.

#### Lost work/mark

Your Test/Quiz paper is missing; mark is wrong or missing
• After Test or Quiz marks are posted on Quercus, I will send an announcement. Please, pick up your paper, check if the mark on Quercus matches the mark on the paper. Also, for the test check that the total mark equals the sum of the marks of the problems. Any problem (missing on wrong mark on Quercus, displaced test paper) should be reported to your TA during this or the next week after posting/distributing papers (extensions are granted upon Class Coordinator's discretion).

#### Remarks

• You can go to any instructor during his office hours.
• You may enroll into any section but you need to stick with your choice.
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