pdf of the Syllabus. Here are the math/stat department policies and the university 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.
Instructor information, including contact information.
My office hours are via zoom Tuesday/Thursday 10:30 - 11:00. If you are my student
I sent you a link via email.
My office is AMB 110, but that doesn't matter much for the remainder of Spring 2020.
Here is my
weekly schedule.
You can always send me e-mail, drop in, or make an appointment if these times aren't convenient.
The requirements for this class are to watch the videos, do the webwork, and do any exams.
April 24: Here are figures of vector fields and eigenvectors: eigenvalues 1 and 2, eigenvalues 1 and -2, irrational eigenvalues, pure imaginary eigenvalues, complex eigenvalues, repeated eigenvalues 0, 0, repeated eigenvalues -1.5, -1.5, and A = 2I with repeated eigenvalues 2, 2. Here is the Mathematica notebook, eigenvectors.nb, that made these figures.
YouTube videos, in reverse chronological order.
The review for the whole course uses 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.)
The Coronavirus Curve
(Not required viewing for our course)
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.
Set 17 problem 11
(A predator-prey system, also called a Lotka-Volterra system.)
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
sample Midterm 2, problem 9
sample Midterm 2, problem 8
sample Midterm 2, problem 11 (helps with set 15)
sample Midterm 2, problem 10 (helps with set 15)
sample Midterm 2, problem 2
sample Midterm 2, problem 1
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
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
Set 12, problem 8
Set 12, Why is y = yh + yp?
Set 12, problem 11
Set 12, problem 5. Here is the link to the desmos graph for
this problem.
Set 12, problem 10. This video is turned sideways!
Sorry about that and I won't let it happen again.
March 10: Here is the handout from today's class about the method of undetermined coefficients.
March 6: Here is page on Solving certain ODE's by inspection, that will help with WeBWorK, set 11, problem 11. This section from Paul's notes (or Boyce and DiPrima section 5.4) will help with set 11, problem 10: Euler Equations, a x^2 y'' + b x y' + c y = 0.
February 26: Summary of the Theory of Linear Homogeneous ODEs.
Note that my office hours for Monday, March 2, are cenceled. I will be in email contact.
February 25: Here is the recipe I wrote on the board to solve a second order linear homogeneous IVP with constant coefficients, provided the roots of the characteristic equation are real and distinct.
February 24: Katherine Johnson, who was featured in Hidden Figures, died today at the age of 101. A web search will find many tributes to this great pioneer. 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, which was posted three years ago on today's date. This is a more nerdy blog about Katherine Johnson's technical note which was mentioned in the film. That blog, like the previous web news story, was posted three years ago today.
February 13: Euler's method scene from Hidden Figures. Here's the (updated) handout from class on how to do Euler's Method with a Spreadsheet.
February 11: Recipe to solve exact ODEs. ALERT! There is an error in that pdf!
The term before h'(y) is wrong, as I mentioned in class.
Here is the corrected equation.
Here is a shorter version of the recipe, that does not have the error of the longer version.
January 28: Recipe to solve any first order linear ODE for y(x). Here's the recipe for y(t).
January 14: Handout on Classification of Differential Equations with solutions.
January 14: 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).
