MAT 239, Differential Equations

Prof. Swift, Fall 2020

pdf of the Syllabus. Here are the math/stat department policies and the university policies and the COVID policies that are technically part of the syllabus.

Here are some graphical resources for differential equations:
Slope Field and Direction Field applet by Darryl Nester of Bluffton University.
Phase Plane applet written by Ariel Barton of the University of Arkansas.

My office phone, 523-6878, goes straight to voice mail.  You can send me e-mail at Jim.Swift@nau.edu. My office is AMB 110, but I will not necessarily be at my office for my "office hours". 

The zoom-meeting-office-hour times are:
Tu 10:30-11:40,
W 3:00-4:00,
Th: 3:00-4:00.
During these times you can join the next zoom class using the regular link. Send me email to let me know you are there and I will join you. (You can also send me email in advance letting me know you plan to come to my "office" hours.)
You can always send me e-mail, drop in to my office and talk to me from the hallway, or make an appointment for a zoom meeting at another time if these times aren't convenient. Here is my weekly schedule which still lists my W and Th office hours ending at 4:30. They now end at 4:00.

Please feel free to contact me in person, by phone or via e-mail with any questions about the math, or with any feedback about the class.

Lecture supplements, in reverse chronological order

Review for Final Exam: Here are YouTube videos to review the whole course. These all use the ODE y' = -3(y-20) as an example for everything!
Review: Systems of Linear 1st Order ODEs (WeBWorK sets 16 and 17.)
Review: Series Solutions (WeBWorK sets 14 and 15.)
Review: Second Order Modeling (WeBWorK set 13.)
Review: Linear ODEs with constant coefficients, and Undetermined Coefficients (WeBWorK sets 9-12.)
Review: Euler's Method (WeBWorK set 8.)
Review: Exact ODEs (WeBWorK set 7.)
Review: Modeling and Autonomous ODEs (WeBWorK sets 5 and 6.)
Review: Linear 1st order ODEs (WeBWorK set 4.)
Review: Intro to DEs and Separable 1st order ODEs (WeBWorK sets 2 and 3.)

November 11: The review for Friday's exam will be a zoom meeting Wednesday at 7:00pm. An email link was sent out via email.

Set 18 problem 5 (Solution to an IVP for a linear nonhomogeneous system.)
Set 18 problem 3 (A nonlinear predator-prey system, also called a Lotka-Volterra system.)

While not required for the course, you might want to look at this youtube video about The Coronavirus Curve
This is a professional video by the awesome "numberphile" about modeling epidemics like our COVID-19 pandemic with a system of 1st order ODEs:
S' = 0 * S - a S I (The British mathematician in the video says "dash" where we say "prime".)
I' = - b I + a S I
This is a preditor-prey system with 0 growth constant for the Susceptible population (the prey, S(t)). The predators in this model are the Infected population, I(t). The Recovered population, R(t), mentioned in the youtube video does not affect the first two populations.

November 4: The solution to x' = A x , x(0) = x₀, with complex or repeated eigenvalues is fast and easy with the ``Swift method". I presented System Solution version 1 in class, but there is also System Solution version 2 where the ``b'' is in a different place. I welcome comments as to which you prefer, or a link to someone else who uses this technique.

Set 17 problem 3, Quick Method This video is new this semester, and uses the method presented in class on Nov. 14.
Set 17 problem 10 computer animation (Normal modes in a mass-spring system.) This video demonstrates the desmos animated graph available here.
Set 17 problem 10 (Normal modes in a mass-spring system.)
Set 17 examples 4 and 5 computer pics (Computer pictures for two matrices with repeated, nonzero eigenvalues.)
Set 17 examples 4 and 5 (Matrix has repeated, nonzero eigenvalues. Like WeBWorK problem 7.)
Set 17 example 3 (Matrix has repeated eigenvalues. Like WeBWorK problem 6.)
Set 17 example 2 computer pics (WeBWorK problem 3 computer pics)
Set 17 example 2 (Complex eigenvalues, WeBWorK problem 3)
Set 17 example 1 computer pics (Computer-generated vector field and solution curves for example 1.)
Set 17 example 1 (Matrix has real, distinct eigenvalues.)
Set 17 intro to problems 1 to 9

Set 16, Eigenvalues example 3 (Eigenvalues of a matrix with parameters.)
Set 16, Eigenvalues example 2 (Complex eigenvalues.)
Set 16, Eigenvalues example 1 (Real eigenvalues.)
Set 16, Eigenvalues and Eigenvectors, Part 2 How to compute eigenvalues and eigenvectors.
Set 16, problems 8, 14 and 15 (Eigenvalues and Eigenvectors, part 1).
Set 16, problems 5-7
Set 16, More about AB ≠ BA
Set 16, Introduction to Systems of 1st Order ODEs, problems 1-4

Set 15, more like problem 1
Set 15, problem 6
Set 15, problem 6 sinc function
Set 15, solving recurrence relation
Set 15, problem 1
Set 15, problem 2

Set 14, problem 8
Set 14, problem 6
Set 14, problems 7 9 10
Set 14, problems 1-5

October 12: In anticipation of the second Midterm on Wednesday, October 14, here are some videos that I made last semester, as the review for the final exam:
Review: Second Order Modeling (WeBWorK set 13.)
Review: Linear ODEs with constant coefficients, and Undetermined Coefficients (WeBWorK sets 9-12.)

October 7: Here are some videos I did about set 13 last semester.
Set 13, problem 6
Set 13, damped oscillator graphs with Desmos graphing calculator . Here are links to the three desmos graphs discussed in the video:
underdamped oscillator, overdamped oscillator, and critically damped oscillator.
Set 13, damped oscillators
Set 13, problem 2 finished
Set 13, problem 2 introduction
Set 13, problem 3 desmos . Here is the link to the desmos graph, polar coordinates for oscillators.
Set 13, problem 3
Set 13, problem 1
Set 13, computing omega_0
Set 13 introduction. Mass on a spring

October 2: Here some videos I did about set 12 last semester.
Set 12, problem 8
Set 12, Why is y = y_h + y_p?
Set 12, problem 11
Set 12, problem 5. Here is the link to the desmos graph for this problem.
Set 12, problem 10.

Sept. 30: Here is the handout from today's class about the method of undetermined coefficients.

Sept. 28: Here is page on Solving certain ODE's by inspection, that will help with WeBWorK, set 11, problem 1. This section from Paul's notes (or Boyce and DiPrima section 5.4) will help with set 11, problem 11: Euler Equations, a x^2 y'' + b x y' + c y = 0.

September 21: Summary of the Theory of Linear Homogeneous ODEs.

September 18: Here is the recipe I wrote on the board in a previous semester to solve a second order linear homogeneous IVP with constant coefficients, provided the roots of the characteristic equation are real and distinct. That semester, I used r instead of k as the variable in the characteristic equation.

September 9: Euler's method scene from Hidden Figures. Here's a pdf on how to do Euler's Method with a Spreadsheet.
I took this screen shot from the Hidden Figures Euler's method Scene, with a descrption of the Modified Euler's method. This method is also called Heun's method, and it is the second method that our Slope Field and Direction Field applet uses. I found this desciption of the role math played in the Hidden Figures movie. This is a more nerdy blog about Katherine Johnson's technical note which was mentioned in the film.

August 28: Here are some youtube videos I made last Spring, as part of a review of the whole course:
Review: Modeling and Autonomous ODEs (WeBWorK sets 5 and 6.)
Review: Linear 1st order ODEs (WeBWorK set 4.)

August 24: Recipe to solve any first order linear ODE for y(x). Here's the recipe for y(t).

August 21: This is a youtube video I made last Spring, and it might help with WeBWorK set 3.
Review: Intro to DEs and Separable 1st order ODEs (WeBWorK sets 2 and 3.)

August 13: Handout on Classification of Differential Equations with solutions.

August 11: Here is an Introduction to WeBWorK. Even if you have used WeBWorK in other classes this has some useful information.
NOTE: You login name and password are those of your LOUIE account (e.g. jws8).