pdf of the Syllabus. Here are the math department policies and the university policies that are technically part of the syllabus.
Marek Rychlik's JOde suite of programs for solving differential equations.
Instructor information, including contact information. My Office hours are MWF 1:45-2:45, TTh 9-10.
Here is the webpage from the last time I taught this class.
Nov. 18 announcement:
We will not have the third exam. There are two new WeBWorK assignments available.
These, along with the homework due Friday, will finish off the course.
The on-line syllabus has been updated. Since the original syllabus says there are three exams,
I will let anyone take the third exam (outside of class time).
Let me know if you want to do this.
It might raise or lower your class grade.
Homework due Nov. 20 (5 class points)
5.2: 4, 8. For problems 4 and 8, do part (a) and (b), but not (c) and (d).
5.3: 2, 6, 10, 12
Here are the scanned solutions.
Homework Due Nov. 16: (5 class points)
5.1: 24
5.2: 2, 6, 15, 16, 21
For problems 2 and 6, do part (a) and (b), but not (c) and (d).
Here are the scanned solutions, and here are the figures for
problem 15 and
problem 16.
Here is the Mathematica notebook that made these figures.
Oct. 28: Mathematica demonstrations of oscillator damping and the sum of sine and cosine.
Oct. 26: Handout on oscillators and complex numbers.
Oct. 21: Here is the handout from class about the method of undetermined coefficients. Here is the same handout with solutions. Don't print this out! I made copies of the sheet with solutions and I'll give it out Friday in class. Here is a scan of the textbook's table of the form of the particular solution. Last time I taught this I did more examples of the form of yp, and less explanation of why. You might like this approach: Here's the old handout.
Oct. 12: Here is some information about the Wronskian and how it relates to the general solution of a linear homogeneous ODE.
Oct. 2: Here is the completion of the example I started at the end of class.
Sept. 25: Here is the handout on Euler's Method that we went over in class.
Sept. 23: Bonus: Mathematica graph of the family of implicit functions that solves my set 6, problem 6. (I did this in class, but didn't show the graph.)
Sept. 21: Bonus: proof of the the solution to the Logistic ODE. Mathematica notebook showing solutions to two population models done in class:
Sept. 18: Here are scanned solutions to the homework and to the extra credit problem. Here are Mathematica demonstrations of the solutions to the IVP and the periodic solution.
Sept. 16:
Homework due at the beginning of class on Friday, Sept. 18.
Section 2.4 # 14, 20, 22 from the textbook (Boyce and DiPrima 9E.) Worth 9 points.
Note: in problem 20, use the JOde
slope field applet. Change from "Euler" method to "RK4" for more accuracy. Do not show "Points" or "Init. Conds"
so your figure isn't too busy. You will also want to change the window (xmin, etc.) to see the behavior
as t increases that the book asks about.
Include a printout of the slope field and several solutions from JOde when you turn in your homework.
Extra credit worth 3 points. (Also due Friday, Sept. 18.)
Let T(t) = A + B cos(t) be the periodic ambient temperature.
Solve Newton's law of cooling for the temperature u(t) of an object.
du/dt = -k (u - T(t)), u(0) = u0.
Separate the solution to the IVP into a periodic solution up(t) of the DE plus a transient solution.
Write the periodic solution in the form
up(t) = A + R cos(t - delta). (Find R and delta in terms of the parameters k and B.)
Discuss approximations to up(t) when k is large or small.
Sept. 16: Mathematica demonstration on the sum of sine and cosine.
Sept. 11: Bonus: A solution to a linear 1st order ODE when you "can't do the integral". Here's a scan of the solution and here's a Mathematica Notebook that plots the solution.
Aug. 24: 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).
