Math 242
Elementary Differential Equations

Mr. Matthew Gamel
Spring 2008


Welcome to Math 242! Please check this page frequently for homework assignments and important announcements.
Course Announcements
Please be aware that the most recent announcements will appear on top.

  • 24 April 2008: I will hold a review session for the final exam on Thursday, May 2 at 5:30PM in our usual classroom. This will essentially be a Q&A session so be sure to have questions. I will also hold office hours on Friday, May 2 from 12:00-1:30PM.

  • 23 April 2008: Our final exam is scheduled for Monday, May 5. I have posted one more homework assignment but it is not mandatory. The material on the final homework assignment WILL be fair game for the final even though I will not collect and grade it. However, should you choose to turn it in, I will give you a few extra points (you need to work the problems anyway when preparing for the final).

  • 27 March 2008: I am behind on grading your homework so the assignment (HW 9) due today can be turned in on Tuesday.

  • 26 February 2008: I am currently sick with the flu so there will be no class today. However, please use this time to prepare for your midterm in a week and work on the homework. The assignment due today has been deferred to Thursday.

  • 21 February 2008: The midterm has been moved to Tuesday, March 4 because I have fallen behind in grading your homework. The same material will be covered.

  • 12 February 2008: The assignment originally due today is due this Thursday, the 14th. Also, we will have our midterm on Thursday, the 28th. It will cover everything we do on first order equations. You have quite a bit of time to study as we will probably end our discussion of first order equations this week. There is no excuse for not being prepared; I will try to have all of your homework on first order equations to you by the end of next week.

  • 30 January 2008: My sincere apologies for not being in the tutoring center today to those who needed to see me. I have been sick as a dog and you probably wouldn't have wanted to be around me anyway. If you need to see me, I will be in my office before class tomorrow. Because I was not in my office today, I will give everyone an extra class day to turn in HW3 on 1st Order Linear Equations; it will now be due on Tuesday, 2/5.

  • 17 January 2008: I have made the following changes to the syllabus in terms of grading policy: homework will count 40%, one midterm will count 25%, and the final exam will count for 35% of your final grade. Please note that the syllabus posted online will reflect these changes.

  • 15 January 2008: Please note that I will announce office hours during lecture next week. Your first homework assignment (consisting of the sheet I handed out in class today) will be due in one week from today.


Contact Information

Email: gamel@math.sc.edu
Office: LeConte 104B

Spring 2008 Office Hours:
Monday/Wednesday Noon-1:00PM in LeConte 105 (tutoring center) Tuesday 3:40-4:40PM in LeConte 104B (my office)


If none of these times are convinient for you, please contact me to make an appointment.

Course Downloads

Here are 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! Please note that if I hand out solutions in class or if I work out the solutions on the board, I am less likely to post them here.
Description
Download(s)
Course Syllabus Course Syllabus
Here is a review of integration for your own benefit; I will not collect and grade these. However, I will be happy to discuss them with you if you feel the need. Integration Practice
Solutions to Graded Problems, HW 4 and 5 Solutions
Information on Final Exam Final Review


Homework Assignments


Please remember that homework will typically be collected one week after it is assigned. The purpose of this chart is to inform you of the various assignments and their due dates so that there is no question as to when they are due. Highlighted assignments indicate those assignments which should be completed. If an assignment is highlighted, it is late.

Assignment
Due Date
Description
#1 (Classification & Verification) 1/22/08 I handed out a worksheet on classification and verification of solutions in class. Please see me if you do not have a copy.
#2 (Existance/Uniqueness & Separable Equations) 1/29/08 I handed out this worksheet in class on existance/uniqueness of 1st order equations and on separable equations. Please note: the due date on the worksheet is incorrect - it is due on Tuesday the 29th, not Thursday the 24th.
#3 (1st Order, Linear Equations) 1/31/08 2/5/08 Page 56 (1-25, 29, 30) Note: The due date for this assignment has been changed. See the 1/30 announcement above.
#4 (Substitution Methods, Bernoulli Equations, & Exact Equations) 2/12/08 2/14/08 Page 74 (17-23, 31-38, 57, 66) Note: You do not need to worry about 16 (that was in the original assignment)
#5 (Homogenous Equations) 2/12/08 2/14/08 Page 74 (1-12) Note: This material comes from the same section as Homework 4 so it will be due on the same day as homework 4. Also, number 4 is extra credit.
#6 (Applications of 1st Order Equations) 2/19/08 Page 43 (33,34,37,38,44,49) and Page 57 (42).
#7 (Linear Independence/Fundamental Sets) 2/26/08 2/28/08 Page 170 (1-5,7-12,13,15,17). To do the last three, remember that a particular solution to a homogenous nth order equation is y=c1y1 + ... + cnyn where {y1, ..., yn} form a fundamental set. You are given the fundamental set to solve for the constants.
#8 (Linear Equations With Constant Coeficients) 2/28/08 Page 183 (1-18, 21, 23, 26)
#9 (Variation of Parameters and Undetermined Coeficients) 3/18/08 Please work this worksheet for homework. This will be due one week from today on Thursday, the 27th.
#10 (Cauchy Euler Equations, Higher Order Nonlinear Equations, Laplace Transforms) 3/28/08 Please work this worksheet for homework. This will be due one week from today on Thursday, April 3.
--- 4/3/08 There will be no written homework to turn in this week so your homework is to study your notes and text on Laplace transforms and Inverse transforms. Become more familiar with them because I will hand out some homework next week.
#11 (Laplace Transforms and Inverse Transforms) 4/17/08 Please work the worksheet that I handed out in class. As this sheet is handwritten, please see me if you need an extra copy.
#12 (Applications of Laplace Transforms and Second Order Equations) 4/23/08 Please work these problems. I will not collect this assignment but you need to know the material on this homework for the final. If you choose to turn this in, I will grade it like a normal homework assignment and give extra points.


Meeting Log

This is an archive of previous lectures in the event that you are unable to attend class. Please note that I am not following the textbook exactly so be sure to obtain notes if you miss class.
Date
Description
1/15/08 Today, I gave you a brief overview on differential equationes and a cursory glance on where and why they arise in applications. We also learned how to classify an equation (that is, we discussed order and linearity) and discussed initial value problems (IVPs) and other types of related problems like boundary value problems (BVPs).
1/17/08 We discussed verification of solutions and then began our discussion on first order equations. We talked about the existance/uniqueness theorem and I gave you an example of an IVP that has more than one solution and explained why the theorem does not apply to that particular IVP.
 
1/22/08 Your first homework assignment was due in class today. In terms of material, we finished talking about existance/uniqueness with a few examples and then I discussed separable equations (basically, this is section 1.4 in your text except we didn't discuss applications). Also, the due date for the worksheet I handed out last time has been moved to one week from today (Tuesday, the 29th). We also began discussing first order, linear equations.
1/24/08 We continued our discussion of first order linear equations and I worked some examples. This is basically section 1.5 in your text.
 
1/29/08 HW2 was due in class today and I handed back your first graded assignment (HW1). Insofar as class is concerned, we finished discussing first order linear equations and talked about Bernoulli's equation (part of section 1.6 in your text).
1/31/08 Today, we continued section 1.6 by discussing substitution methods and exact equations. I will work more examples of exact equations next time but you should begin the homework assignment early. Also, there is a slight error in the statement of Theorem 1 in your text (p 70). It is necessary for the mixed partial derivatives to be continuous as stated on page 69. This will not impair your ability to do the homework; rather, I am mentioning this for the sake of being complete.
 
2/5/08 HW 3 was due in class today. Today, I furnished one more example of solving an exact equation and we then discussed homogenous equations. The material from the last few days has been from Section 1.6 in your text.
2/7/08 Today, we spent the entire time discussing applications of first order equations.
 
2/12/08 The due dates for HW 4 and HW 5 have been moved to Thursday. Today, we started discussing higher order equations; we reformulated our IVP in the form Ly=f and discussed linear dependence/independence.
2/15/08 HW 4 and HW 5 is due today. We finished discussing linear independence by talking about the Wronskian determinant and we began discussing reduction of order.
 
2/19/08 Today, we discussed reduction of order and then we discussed solution methods for general nth order linear equations with constant coeficients.
2/21/08 I worked more examples of solving constant coeficient higher order equations and we began discussing solution techniques for constant coeficient non-homogenous problems. We primarily discussed the method of undetermined coeficients but have not concluded our discussion. We will finish undertermined coeficients next time.
 
2/26/08 Today, I am currently sick with the flu so there will be no class. Consider this a catch-up day if you have managed to fall behind.
2/28/08 Today, I am currently sick with the flu so there will be no class. Consider this a catch-up day if you have managed to fall behind.
 
3/4/08 You took your first midterm today.
3/6/08 We finished the method of undetermined coeficients today and discussed variation of parameters.
 
3/11/08 SPRING BREAK, No Class. Have a safe and restful break. There was no homework assigned during this time because I managed to catch the flu again this week.
3/13/08 SPRING BREAK, No Class. Have a safe and restful break. There was no homework assigned during this time because I managed to catch the flu again this week.
 
3/18/08 Today, I worked one more example on variation of parameters and we discussed solution methods for Cauchy-Euler equations and certain types of second order nonlinear equations. Please note that I have assigned a new homework assignment.
3/20/08 We began discussing Laplace transforms today. We primarily discussed the definition and then derived the basic formulas using the definition.
 
3/25/08 We continued to discuss Laplace transforms. I worked some more examples and we talked about the First Translation Theorem. I will give a few extra bonus points for a proof.
3/27/08 Today, I discussed a few of the homework problems briefly and then informed you that I am a bit behind on the grading so you can keep the current problem set and turn it in on Tuesday. Insofar as material is concerned, we discussed Heaviside functions and the Second Translation Theorem pertaining to Laplace Transforms.
 
4/1/08 We began our discussion of inverse transforms. We finished by discussing how we might use the first translation theorem to compute a transform.
4/3/08 We began with another example of using the first translation theorem to compute an inverse transform and discussed convolutions and the convolution theorem.
 
4/8/08 I handed out a worksheet on Laplace transforms for you to chew on for a week or two. It will be due on Thursday the 17th, despite the fact that the sheet says it is due on Tuesday, the 15th. We talked about using Laplace transforms to solve differential and integral equations.
4/10/08 We continued our discussion of using transforms to compute solutions to differential equations and I decided to let the class out early today.
 
4/15/08 I began class by working on problem 19 from your worksheet; you need to use the convolution theorem to solve this. I also presented an alternate solution which required one to make several astute observations. Other than this, we began our discussion of undamped, free motion of a spring system.
4/17/08 We continued our discussion of undamped, free motion and also discussed what happens when we add a damping force to the system.
 
4/22/08 We discussed LRC circuits today in class.
4/24/08 Today is the last official day of class. We discussed the final exam and filled out course evaluations. We also scheduled a review session for the final on Thursday, May 1 at 5:30 in our usual room (if our usual room cannot be reserved, I will find a room). The review session will be just like a Q&A session - you ask me questions and I will answer them. I will also hold office hours on Friday, May 2 from 12:00-1:30.