Math 242
Elementary Differential Equations |
Matthew R. Gamel
Summer I 2007
Welcome to Math 242! Please check this page frequently for homework, course updates, and
announcements. If you have any questions, please do not hesitate to
contact me. I wish each of you a productive and informative semester/session!
Here are the various course downloads. You will need some way to view PDF files
(ie. Acrobat for Windows/Mac users, XPDF for UNIX). If you have trouble reading these files,
please contact me ASAP!
Remember to check back often for due dates and new assignments. You may collaborate with your peers on the homework assignments but you MUST
submit your own work. Remember that late assignments will generally not be accepted.
| Assignment
|
Due Date
|
Description
|
| 1
|
6/11/07
|
Integration Homework
|
| 2
|
6/7/07
|
See handout from class; this homework concerns classification of ODEs and verification
of solutions.
|
| 3
|
6/11/07
|
See handout from class; this homework is on existence/uniqueness of first order equations and
separable equations. Please note that on the worksheet, the listed due date is Friday by 5PM but I moved this to Monday.
|
| 4
|
6/13/07
|
See handout from class; this homework is on first order, linear, nonhomogenous equations,
substitution methods for first order equations, and Bernoulli equations.
|
| 5
|
6/25/07
|
This may be downloaded here and covers second
order equations. Please Note: This is quite a bit of work so please start early. There may be one more homework to be handed out this week (it
will most likely be due on Tuesday of next week).
|
Please be aware that the most recent announcements will appear on top.
20 June 2007: Number 5d in the solutions to homework 3 was copied down incorrectly. The version that is there was
solved correctly but it is not the one from the homework. This problem has not been graded for that reason. Also, please download
homework 4 again as I made some corrections to errors.
4 June 2007: Welcome to Math 242! Please read the course syllabus carefully and ask me if there are any questions. Also, please
note that I will be out of town next week (starting Monday the 11th thru Friday the 15th). Homework will still be collected by your substitute so please
check the website frequently for assignments and due dates. Finally, next wednesday (the 13th), you will have your take-home midterm (there will be
no class on Thursday). It will be due on Monday the 18th, no exceptions.
This is an archive of what we have talked about and did each class day. If you missed
a class meeting, please make sure to obtain course notes from a fellow classmate.
| Date
|
Description
|
| 6/4/07
|
We discussed course procedure and proceeded to discuss the taxonomy of differential equations.
We also discussed verification of solutions.
|
| 6/5/07
|
We briefly discussed a version of the existence/uniqueness theorem for first order
equations and talked about separable equations. I also made a few remarks about Newtonian mechanics and certain population models that may be modeled by
differential equations.
|
| 6/6/07
|
Today, we discussed solution techniques for general, first order, linear, nonhomogenous
equations and discussed Bernoulli's equation.
|
| 6/7/07
|
Your first homework was due today. Today, we continued to discuss Bernoulli equations and
then we discussed solution of 1st order equations by substitution. I answered some questions and we wrapped up a bit early today.
|
| 6/11/07 thru 6/13/07
|
You had a substitute (Pavel Zeltov) and covered linear dependence/independence,
n-th order linear homogenous equations with constant coeficients, reduction of order, and the method of undetermined coeficients. The integration
homework and homework 2 were due on Monday while homework 3 was due on Wednesday.
|
| 6/18/07
|
Today, we discussed variation of parameters and Cauchy-Euler equations.
|
| 6/19/07
|
Our primary task today was review of second order equations. I
also answered some questions pertaining to the homework assignment. |
| 6/20/07
|
Today we began the section on Laplace transforms. We discussed the
definition and learned how to compute the Laplace transform for elementary functions.
|
| 6/21/07
|
We discussed the first and second translation theorems and briefly
tackled the question of existance of Laplace transforms.
|
| 6/25/07
|
Today, we mainly discussed methods of computing inverse Laplace transforms.
Please note that the upcomming homework is due next Monday. Also, there will be no final; rather, your grade will be based on homework and
attendance.
| 6/26/07
|
Our discussion of the Laplace transform has finally been put to use today
as we learned how to use the Laplace transform to solve differential equations. We also discussed the Convolution Theorem and how it pertains
to computing Laplace transforms.
|
|
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