Math 2280 - Differential Equations

• May 6th The final exams are now graded, and your final exam scores, as well as your final class percentages and letter grades, are now available on WebCT. Please contact me before May 15th if you'd like to go over your grade, pick up your final exam, or discuss anything else with me. Also, the final exam and solutions are posted below. Thank you for a great semester, and good luck in all you do. -Dylan


• April 28th Today was our last day of lecture. I went over a few longer and more involved example problems from chapters 8 and 9. We'll have our review session for the final exam on Thursday from 4:30 PM until 6:30 PM. Also, there were some errors in the lecture 25 notes. I corrected them while I was lecturing, and they've since been corrected in the notes, but if you downloaded the notes before the lecture there were some errors.


• April 23rd Today we finished covering sections 9.1 through 9.3 of chapter 9, which will be as far as we go in the textbook. Next Tuesday, for our last class, I'll just do a few more involved example problems from chapters 8 and 9, and then open up the rest of the time for questions.


• April 21st Today we finished covering section 8.4, which covers series solutions around regular single points. I've decided that the homework for section 8.4 is optional. The solutions will be posted, and I will grade the homework for that section, but it will be for extra credit. We also started section 9.1 today. We'll be covering sections 9.1 through 9.4 in chapter 9 before the end of class. Also, we'll be having our review session for the final on Thursday, April 30th from 4:30 PM until 6:30 PM. Location to be announced.


• April 16th Today we had our third exam during class.


• April 14th Today we covered section 8.3 and began covering section 8.4 of the textbook.


• April 9th Today we began our study of series solutions of ODEs, covering sections 8.1 and 8.2. We will have our exam next Thursday, April 16th. The exam will cover sections 5.4 throuth 5.6, and chapter 7. We'll have a review session in room 323 of LCB from 4:30 PM to 6:30 PM on Wednesday, April 15th.


• April 7th Today we covered nonlinear biological and mechanical models. We'll be starting series solutions to ODEs next time.


• April 2nd Today we covered behavior around critical points for two dimensional linear systems, and how this applied to the behavior of nonlinear systems around critical points. This is section 6.2 from the textbook. Also, we decided that the exam originally scheduled for next Thursday would be postponed one week.


• March 30th I had to only have half a class today. We finished covering Laplace transforms, and began chapter 6. We made it through most of section 6.1 today. Please note my office hours tomorrow will be in the LCB computer lab.


• March 26th We covered sections 7.5 and 7.6 of the textbook today, which finishes up chapter 7. Please note that I extended the due date for the second project, so it's now due next Thursday, April 2nd. Also, I've posted an explanation below for one of the tricky steps in the project.


• March 24th Class was cancelled today because of a gas leak. So, we'll cover what we were going to cover today on Tuesday. Please note that on problem 33 of section 5.4 there is a typo. The vector v2 should be [0 0 1 i], not [9 0 1 i].


• March 12th Today we had our second exam. It was probably a bit too hard. Sorry. I'll grade them over the break. Have a nice spring break everybody.


• March 10th Today we covered partial fraction decompositions and how to find inverse Laplace transforms of rational functions. Then we covered convolution products and their relation to Laplace transforms, and reviewed some other properties of the Laplace transform.


• March 5th Today we began the chapter on Laplace transforms by covering sectiosn 7.1 and 7.2 We're going to be covering chapter 7 before we cover chapter 6, and so we won't be doing chapter 6 until after spring break. Assignment 7 was due in class today. Also, our second programming project should be posted next week.


• March 3rd Today we finished chapter 5 by covering sections 5.5 and 5.6. Section 5.5 is the section on matrix exponentials and their relation with systems of differential equations. Section 5.6 is the section on nonhomogeneous first order systems, and methods we have for finding particular solutions to these systems. We note that our second exam will be on Thursday, March 12th and will cover everything we covered in class from section 3.1 through section 5.3. There will be a review for the exam on Wednesday, Marh 11th in liu of my usual office hours, location to be announced when I know the location. Also, I'm going to try to type up lecture notes for lectures 9, 10, and 11 this weekend.


• February 26th Today we covered sections 5.3 and 5.4, on second-order mechanical systems and their solutions, and on what we do if we have repeated eigenvalues in our coefficient matrix. Assignment 6 was due today, as was the first project. The second computer prorject will be assigned next week. Also, please note that I did not assign homework problems from sections 3.6 and 3.7. I've added some recommended problems below from these sections, and I'll be posting solutions to these recommended problems, but you don't have to work them yourselves. However, you may see a question from one of these sections on the second exam, so you should try the recommended problems.


• February 24th Today we covered sections 5.1 and 5.2. Most of the first hour was a review of linear algebra, which I gathered was boring for all involved. Sorry. As for the second part, we covered the notion of how we express first-order linear systems as matrix equations, and then covered how we can solve these systems if the coefficient matrix is all constants using eigenvalue methods. Finally, please note that I'll be doing my best to get the posted lecture notes all caught up and updated by about a week before the next exam. The solutions to assignment 5 are now posted below. Finally, please note that Wednesday, February 25th is the last day to fill out the midterm evaluation. If you haven't done so yet, please do! Thanks.


• February 19th Today we covered sections 4.1 and 4.2 from the textbook, and assignment 5 was due in class today. Please don't forget to fill out the evaluation. Also, the solutions for assignment 4 are now posted below. I'd like to apologize for that assignment, as it was very tedious.


• February 17th Today I handed back assignment 3 and the first exam. Please note that there was a grading error for some people on problem 3a, so if you got 4 points out of 5 please ask me about it, you may deserve 5 points out of 5. In class we finished section 3.5, and covered sections 3.6 and 3.7. Assignment 5 is due in class next time, and assignment 6 is now posted below.


• February 16th Please note that the writeup for the first project has been modified to specify that for the improved Euler's method part you should find the values out to five decimal places, and for the Runge-Kutta part you should find the values out to nine decimal places.


• February 12th Today we covered most of section 3.5 and then had our first exam. The exam should be graded this weekend.


• February 10th Today we covered sections 3.4 and most of section 3.5. The solutions to assignment 3 are now posted below, and please note that assignment 4 is due next time. Our first exam will be during the second hour of class next time.


• February 5th Today we covered sections 3.2 and 3.3. Assignment 3 was due today, and please note we'll be having our first exam on Thursday, Febraury 12th. It will cover everything we've covered in the first four assignments, so every section from chapters 1 and 2 that we've covered in class. The exam will be an hour long, and will take place during the second hour of class. Also, please note that my tutoring center hour is determined, and it's on Mondays from 10:00 AM to 11:00 AM. Finally, I've posted some review material for the first exam below.


• February 3rd Today we finished covering numerical methods (yeah!) by going over the Runge-Kutta. Also, we covered section 3.1, which introduced us to second order linear ordinary differential equations. Also, please note that my office hours tomorrow will be from 3:00 PM until 5:00 PM, not from 4:30 PM until 6:30 PM.


• January 29th Today we went over Euler's method and the improved Euler's method. Assignment 2 was due today. Also, I didn't hand out the first programming assignment, which will be posted on the web on Tuesday.


• January 27th Today we had our first day of class in our new room, ST 208. I covered sections 2.2 and 2.3 of the textbook. I announced that on Thursday assignment 2 will be due, and I'll be giving out the first Maple project description. Also, I've decided to write up my own lecture notes from here on our instead of using Prof. Korevaar's, so you'll notice a change in the lecture notes posted below. Also, assignment 3 is now posted.


• January 22nd Today we finished section 1.5 of the textbook and also covered section 2.1. The first assignment was due today as well.


• January 20th We had a shorter day today and only covered through section 1.5 of the textbook. We went over first-order linear ODEs today and the formulas used for solving them. We also discussed the corresponding existence and uniqueness theorems, and then worked a number of examples. Please note that next week we'll be in a different classroom, and that my office hours on January 21st will be in the computer lab.


• January 15th We had our second day of class today. We covered sections 1.3 and 1.4 and finished the first week of lecture notes. Next week I'll be having my office hours in the computer lab, and we might also have one of our classes there as well. Finally, I'm going to put in a request for a different classroom, as I think ours is too cramped and too hot. I'll let you know if and when we get a new classroom.


• January 13th We had our first day of class today. We covered the syllabus and the first two days lectures from the lecture notes. The first assignment is posted below. Also, my first office hours will be tomorrow evening.


• January 12th The website is now up, which I suppose is obvious given you're reading this. Our first class is tomorrow (Tuesday) evening, but if you'd like to find out what we'll be doing, please check the syllabus.

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