Course Notes
MAT2384
Ordinary Differential Equations
 Ω 
Experimental Failure
Regrettably, I could not keep up (as those around me warned) with the task of copying summaries of every lecture I attended, complete with MathJax and diagrams, into markdown files.
While it lasted, it was a fantastic way to review and reinforce my learning. I'll leave these MAT2384 course notes up, but they will now be accessible via the archives.
I would absolutely attempt this again, but perhaps on a weekly basis.
Table of Contents
 Preamble
 Syllabus
 Important Dates & Deadlines
 Lecture Notes
 Side Effects
 References
Preamble
I took MAT2384: Ordinary Differential Equations during the Winter 2019 Semester. The notes below were recorded over the duration of the course, after each lecture. Each section anchor is hyperlinked in the table of contents above. References and footnotes are present^{1} and can be found at the end of the document.
Syllabus
ODE covers the mechanics and usage of Ordinary Differential Equations, Numerical Methods and Laplace Transforms. The textbook used is written by uOttawa’s own Steven Desjardins and Remi Vaillancourt. Chapters 14 and 6 cover ODEs, 5 covers Laplace Transforms, and 710 covers Numerical Methods. Section C is being taught by Tanya Schmah (tschmah@uottawa.ca). Course timeline and materials can be found at http://mysite.science.uottawa.ca/tschmah/mat2384c.
The final is worth 50%, and a minimum grade of 40% must be scored on the final to pass.
Important Dates & Deadlines
Date  Event 

20190123  Assignment 1 due 
20190206  Assignment 2 due 
20190227  Assignment 3 due 
20190304  Midterm exam 
20190313  Assignment 4 due 
20190327  Assignment 5 due 
Lecture Notes
Winter 2019 lectures run from January 7th to April 5th; the second week of the year through to the end of week fourteen. Lecture notes are labeled according to week, then by day/lecture. My schedule for this class/year is as follows:
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
PreLecture Notes
Each week entry is filled with the material that will be covered in the coming week, to review on the weekendof. Each event entry should contain a summary of the learning and notes.
MathJax has been included for the presentation of formulae and mathematics, tutorial here.
It can be written inline, like so:  pretty neat. The primary means of inclusion will probably be in a block, to present formulae:
A more detailed example:
$$
\begin{align}
\int \frac{dy}{y} =  \int 2x \, dx + c_{1}
& \Longrightarrow ln y = x^2 + c_{1}\\
y(x) & = e^{x^2 + c_{1}} = e^{c_{1}} e^{x^2}\\
y(x) & = c \, e^{x^2}
\end{align}
$$
My New Year’s Resolution is to keep these course pages up to date throughout the Winter semester. With any luck, I’ll have a great resource to look back on, and the extra work I put in to demonstrate my knowledge here will pay off on the assignments and exams.
W02 January 0612
Monday 1730h  Double Lecture in SITE B0138  1.1, 1.2, 7.4
The lecture on Monday is split into a full session of ODE, and 50 minutes of Numerical Methods. The ODE portion of the lecture covered ODEs and PDEs, and the order of ODEs. Numerical Methods covered Fixed Point Theorem, and mentioned that the Intermediate Value and Mean Value Theorems from Calculus had to be reviewed.
An ODE is an equation containing one or more derivatives of a function.
The first class of ODEs are Seperable ODEs. They can be expressed in the form , or . The general solution to a Seperable ODE is:
I need to put a lot of work into reviewing basic integration and differentiation.
Fixed Point Iteration was covered during Numerical Methods, and can be found on p.162 (Desjardins), Section 7.4.
Wednesday 1600h  Lecture in SITE B0138  1.3
Missed this lecture due to CUSEC conference, but Section 1.3 was covered.
Section 1.3 involves Homogenous Coefficients. Notes will be placed here soon.
W03 January 1319
Monday 1730h  Double Lecture in SITE B0138  1.4, 7.5
 Homogeneity
 Checking for exact ODEs.
Numerical Methods: Chapter 7.5:
 Intermediate Value Theorem.
 Fixed Point Iteration.
Wednesday 1600h  Lecture in SITE B0138  1.5
 Exact & NonExact ODEs, how to handle both.
W04 January 2026
Monday 1730h  Double Lecture in SITE B0138  1.6, 8.1
Wednesday 1600h  Lecture in SITE B0138  2.1, 2.2
W05 January 27  February 02
Monday 1730h  Double Lecture in SITE B0138  2.36, 8.1
Wednesday 1600h  Lecture in SITE B0138
Practice questions posted at aix1.uottawa.ca/~jkhoury
W06 February 0309
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
W07 February 1016
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
W08 February 1723
Reading week. Study for midterm.
W09 February 24  March 02
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
W10 March 0309
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
W11 March 1016
Monday 1730h  Double Lecture in SITE B0138
Wednesday 1600h  Lecture in SITE B0138
Finish lecturing on systems of ODEs.
Side Effects
Interesting experiments that occur as a result of knowledge gained in the classroom will be documented here, if any are completed.
Useful MathJax Statements for ODE
Prime X'
, fractions \frac{dy}{dx}
.
Partial derivatives \frac{\partial y}{\partial x}
.
Roots \sqrt{x^3}
and \sqrt[4]{x^3}
.
Greek letters like \epsilon \varepsilon
or \phi \varphi
.
Domains can use \mathbb{R}^2
.
\Im \Re
\infty \aleph_0 \nabla \partial
.
$$
\int g(y) \, dy = \int f(x) \, dx + c
$$
Aligned at the primary =
or =>
:
$$
\begin{align}
\int \frac{dy}{y} =  \int 2x \, dx + c_{1}
& \Longrightarrow ln y = x^2 + c_{1}\\
y(x) & = e^{x^2 + c_{1}} = e^{c_{1}} e^{x^2}\\
y(x) & = c \, e^{x^2}
\end{align}
$$
Matrix:
$$
\begin{bmatrix}
a & b & c\\
d & e & f
\end{bmatrix}
\, \dot \,
\begin{pmatrix}
a & b & c\\
d & e & f
\end{pmatrix}
$$
MathJax is wicked.
References

Footnotes are used by placing
[^ref]
where a superscript number should be placed, and[^ref]: explanation
can be used inplace or at the end of the document. All referenced footnotes will be collected and placed at the end of the document. More info. ↩
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