# 21-260: Differential Equations

### Description

The subject of differential equations can be described as the study of equations involving derivatives. It can also be described as the study of anything that changes. The reason for this goes back to differential calculus, where one learns that the derivative of a function describes the rate of change of the function. Thus any quantity that varies can be described by an equation involving its derivative, whether the quantity is a position, velocity, temperature, population or volume.

There are three main ways to study differential equations. There are analytic methods, wherein a mathematical formula for a solution of a differential equation is obtained. There are Numerical techniques, which provide an approximate solution, generally using a computer or programmable calculator. Differential Equations can also be studied qualitatively, determining general properties of solution without concern for exact behavior.

In this course, we will emphasize analytic methods, though qualitative and numerical techniques will make brief appearances.

### News

Tuesday 15 May:

Friday 11 May:

I've been fielding quite a few questions along the lines of "I see that there is an average score for HW#15, but I don't have a grade recorded. Did my homework get lost?" I just want to assure you that only a small number of the HW#15 grades have been recorded. (One or two sections, maybe.) So you should not be alarmed by this.

The TA's all have final exams and projects as well, and some have been getting their grading done early, while others have been waiting until after their exams early this week. I hope to have all the grades assigned and submitted on Monday or Tuesday next week.

Saturday 6 May:

1. Solutions to the last homwork asignment (HW#15) are now available outside my office door.
2. At yesterday's review session, I was asked what you will need to know about the matemtaical models we studied using first order differential equations. I could think of four main things Newton's Law of Eooling and the exponential growth and decay models. You should have these memorized (i.e. the differential equations, method of solution, and applications). You should be able to recognize a logistic growth model, and be able to come up with the differential equation with some prompting. You should not memorize Torricelli's law.

Friday 5 May:

I'll be in my office for about an hour on Sunday, from 11:30-12:30. IF you have any last questions you would like answered, I'll try to do so.

Friday 5 May:

I'll hold a Review Session on Saturday, May 6, from 1:00-2:30pm in DH 2315.

Friday 5 May:

Today's class demonstration is available here. It shows the signal produced by an amplifier with a maximum output amplitude of 1, when it is fed a signal with amplitude A. The stars along the bottom represent the energy contributed by the first 10 harmonics.

Tuesday 1 May:

I've added Section 10.1 to the list of sections covered on the final, and included a couple sample problems from that section. These were erroneously left off before.

Saturday 28 April:

I've posted some review materials for the final exam. You can follow the link from the schedule page. Note that the final exam is a cumulative exam, thought the material that was not covered on the three midterm exams may receive some emphasis.

Saturday 28 April:

The reading and homework for Week #15 have been posted. Follow the link from the schedule page.

Homework #15 is due on the last day of class. Our final exam follows hot on it's heels -- First thing Monday morning. I don't know that the homework can be graded by then, but I will make sure that solutions to HW#15 are available over the weekend. Because of this, I will not be able to accept late homework for this last assignment.

Tuesday 17 April:

There is no homework assignment for Week #13. The reading and homework for Week #14 have been posted. Follow the link from the schedule page.

Tuesday 17 April:

Well, I was looking at the state of our course, what we've covered recently and our schedule this week. I had initially intended to assign homework due Wednesday this week. Since I cancelled class that day, compensating for our early morning exam, that doesn't seem to make much sense. Monday is the next possible day, but that is right after carnival. I could make the assignment due a week from Wednesday, but then would I have another assignment due two days later?

Ultimately, I decided that there will be no homework assignment for this week. I'll just lump this week's and next week's assignment together and make it all due a week from Friday, i.e. April 27. It will be a bit longer than usual, so you may want to start on it earlier than usual.

Monday 16 April:

I've updated the statistics for the course to include the results of Exam #3.

I am frequently asked, "What do the letter grade cutoffs mean for my final grade?" or words to that effect. To get the cutoffs for final grades, the A cutoff for example, I simply average the A cutoffs for each assignment, just like I average your grades. You can see the current grade cutoffs in the top section, labeled "Cumulative Average."

Wednesday 11 April:

I will hold a review session tonight from 6:30-8:00 in DH 2210. You can ask whatever questions you may have then.

Tuesday 10 April:

I've added some old exam problems to the Exam #3 review page.

Firday 6 April:

I've posted a review page for Exam #3, which will be held next Friday, April 13, from 7:30-8:20am in UC McConomy. You can find the link on the schedule page. I'll update it with old exam problems when I get a chance.

Monday 2 April:

I've updated the statistics for the course to include the results of Exam #2. I am frequently asked, "What do the letter grade cutoffs mean for my final grade?" or words to that effect. To get the cutoffs for final grades, the A cutoff for example, I simply average the A cutoffs for each assignment, just like I average your grades. You can see the current grade cutoffs in the top section, labeled "Cumulative Average."

Friday 30 March:

The reading and homework for Week #10 have been posted. Follow the link from the schedule page.

Wednesday 28 March:

Exam #3 will be held on Friday, April 13 in McConomy Auditorium at 7:30am. I had changed the date to better accommodate Spring Carnival schedules, but I guess I didn't get the word out very well.

Monday 26 March:

The reading and homework for Week #10 have been posted. Follow the link from the schedule page.

Saturday 17 March:

Exam #2 will take place on Wednesday, March 21. The exam will be held during the normal class times, 10:30-11:20 or 12:30-1:20. The exam will not be in the usual classrooms, however. It will be held in McConomy Auditorium.

I've posted a review page for Exam #2. Follow the link from the Schedule page. The exam covers Chapter 7 in the text (Systems of differential equations). The specific sections, as well as review problems from the text are listed on the review page. The review page also provides some exam questions I've posed to my 21-260 students in previous semesters. Note that soltuions to the old exam problems will not be distributed. You have lots of problems with solutions available in the textbook, and I think it is important for you to get used to working through problems without having the solution available as a reference. You are certainly welcome to ask your TA or me about these problems.

I will hold a review session on Monday evening, from 6:30-8:00pm in DH 2210. That will be a good opportunity to ask questions about the old exam problems.

Tuesday 6 Friday 16 March:

It seems that last week I did alsmost everything necessary to post this upate. Well, it's here now.

I've posted a review page for Exam #2. It's not yet complete, but it shows what sections will be covered, and gives review problems from the text. I still have to get together some old exam problems, and schedule a review session. You can find a link from the Schedule page.

Thursday 1 March:

The reading and homework for Week #8 have been posted. Follow the link from the schedule page. Note that because of the mid-semester break, the homework will be due on Thursday this week. You can turn it in to your TA during recitation or put it in your TA's mailbox by 3:20 on Thursday 8 March.

Tuesday 27 February:

For problem 7.4.2 on this week's assignment, you should skip part (d). Do only parts (a), (b) and (c).

Monday 26 February:

I've posted the home-made problems for this week's assignment. Try refreshing your browser if you don't see the link.

Last Friday, I started class with an announcement of a problem solving contest. If you are interested in participating, you can go to the Spring Problem Solving Contest website for more information.

Friday 23 February:

The reading and homework for Week #7 have been posted. Follow the link from the schedule page.

Tuesday 20 February:

Here is a link to some statistics for the course.

Sunday 18 February:

The reading and homework for Week #6 have been posted. Follow the link from the schedule page.

Monday 12 February:

I'll be holding a review session tonight, from 8:00-9:30pm. It will be held in DH 2315. This will be a good chance for you to ask questions about the review problems.

Wednesday 7 February:

You should also check this blog post for some other helpful comments related to this week's assignment.

On the assignment for this week, problems 7.3.6 and 7.3.10 deal with linear independence of vectors, which we did not get to cover yet. Consequently, I have removed them from the assignment. They will reappear on the next assignment (after next week's exam).

I've posted a review page for Exam #1. I lists the sections that will be covered on the exam, gives suggested practice problems from the text, and provides some old exam problems. These are problems I have written myself and given to actual 21-260 students, so they should give a pretty good idea what you will be faced with on exam day. You can find a link to the review from the Schedule page.

Friday 2 February:

The reading and homework assignments for Week #4 have been posted. Follow the link from the Schedule Page.

Pietro Siorpaes will hold office hours on Mondays and Thursdays from 10:30-12:00, or by appointment.

Monday 29 January:

I've made a correction to the Staff page. Raja Ahmad's office is in WEH 7215, not PPB 342, as originally stated. Sorry about that confusion.

Saturday 27 January:

The reading and homework assignments for Week #3 have been posted. Follow the link from the Schedule Page.

Thursday 25 January:

My office hours on the Staff page have been corrected. (They were a holdover from a previous semester.) The corrected office hours are Tuesday from 10:30-12:20 and Wednesday from 1:30:3:20.

Wednesday 24 January:

The Final Exam has been scheduled for Monday 7 May, from 8:30-11:30am in UC McConomy. Please take this into account when making your travel plans.

Academic Development has scheduled a Time Management Workshop for Thursday, February 1st from 8:00 p.m. - 9:00 p.m. You can register online, via email or by phone (412-268-6878).

Monday 22 January:

My office hours this semester will be Tuesday from 10:30-12:20 and Wednesday from 1:30:3:20.

I've made a slight modification to the homework exercises for Week #2. I've removed 1.1.27 and 2.1.15 from the assignment, and added 1.2.16, 2.3.4 and 2.3.8. You can follow the link from the Schedule page to find the updated assignment.

I've also removed 2.2.22 and added 2.3.6.

Saturday 20 January:

The reading and homework assignments for Week #2 have been posted. Follow the link from the Schedule Page. You will have to take a short tour of the Policies page before you can view the Exercises.

Tuesday 16 January:

Since Lecture 2 (12:30) did not meet on Monday, due to the half-holiday, I'm going to cancel the 10:30 (Lecture 1) lecture on Wednesday. This will make sure that the two lectures stay on the same schedule.

I announced this at the end of class yesterday, but I want to make sure the word gets out.

Sunday 14 January:

The reading and homework assignments for Week #1 have been posted. Follow the link from the Schedule Page. You will have to take a short tour of the Policies page before you can view the Exercises.

Friday 12 January:

During the first few weeks of the semester we will be jumping aroung in the textbook quite a bit. In order to give a more coherent presentation, I've written up these notes. They are definitely "rough around the edges," but I think they will be useful, especially to read over after attending the lectures.

Monday 8 January:

Welcome to the Differential Equations Website.