21-260: Final Exam

I've posted a review page for the Final Exam. You can follow the link from the Schedule page.

21-260: Week #15

The reading and homework assignments for Week #15 have been posted. You can follow the link from the Schedule page.

Hello World!

Conor Thomas Handron was born at 6:10am on Monday, November 26.

21-260: Week #14

The reading and homework assignments for Week #14 have been posted. You can follow the link from the Schedule page.

21-260: Week #12

The reading and homework assignments for Week #12 have been posted. You can follow the link from the Sceudule page.

21-260: Week #11

The reading and homework assignments for Week #11 were posted a few days ago. Sorry for not announcing it here before now. You can follow the link from the Schedule page.

21-260: Week #10

The reading and homework assignments for Week #10 have been posted. You can follow the link from the Schedule page.

21-260: Week #8 Solutions

I've posted the solutions to HW#8. You can find them on the "Solutions" page of the Blackboard site.

21-260: Exam #2 Review

Three of the problems listed from the textbook ought not to have been. Problems 7.1.2, 7.1.4 and 7.1.6 all deal with second order differential equations, which we have not yet covered. You can safely ignore them. Also, I will hold a review session this evening from 6:30-8:00 in PH 100.

Exam #2 Review Problems

I've added another large collection of review problems to the exam review page linked from the Schedule page. Also, be sure to look at the homework solutions posted on the Blackboard site.

21-260: Week #8

The reading and homework assignments for Week #8 have been posted. You can follow the link from the Schedule page.

21-260: Week #7

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

21-260: Week #6

The reading and homework assignments for Week #6 have been posted. You can follow the link from the Schedule page.

21-260: Week #5

I've posted the reading and homework assignments for Week #5. As I mentioned in class, there is no written assignment this week. There is an online assignment. I said in class that it would be due on Friday, but I've changed the deadline to Sunday evening, because... Well because there was no reason not to.

You can follow the link from the Schedule page.

21-260: Study Break

Engines of our Ingenuity.

21-260: Exam Strategy

I just responded to a student email asking about studying for the exam, and what type of exam you can expect. This is what I wrote:

I would say that working through practice problems is the best way to prepare. You should also review your class notes, and especially your graded homework. When you are working problems, keep track of things you need to look up or ask about. Those are things you should focus on as the exam date gets closer (as it is now!)

On the day of the exam, I would recommend taking a couple minutes to read over the whole exam. Sort out which problems look easy, and which look more challenging. Finish the easiest problems first, leaving you more time to think about the harder problems without distractions.

Regarding the makeup of the exam. You can expect 20-25% of the exam to be pretty straightforward, and another 20-25% to be pretty challenging. The rest somewhere in between. There will be some conceptual material, like on the written homeworks, but most of the exam will be more computational.

Chris Potter's office hours

My office hours this week will be in Wean 6201:

Mon 4-6pm
Tue 2-4pm
Wed (none)
Thu 4-5pm

21-260: Exam Odds and Ends

As announced in class today, our first midterm is this Wednesday from 7:30-8:20 in UC McConomy. There will be no class on Wednesday. I will hold a review session tonight from 6:30-8:00 in PH 100.

I've added "Systems of Differential Equations (Section 7.1)" to the list of topics covered. That is what I've been telling people all along, but I inadvertently left it off the list. I also added 7.1.23 to the practice problems from the text.

21-260: Week #3 Homework Solutions

... are now available in the Solutions section of the Blackboard site.

21-260: Week #4 WileyPLUS Assignment

I've had to remove two problems from the WileyPLUS assignment for this week. Problems 2.7.1a and 2.7.18b were left over from a previous version of the course. We are not covering Euler's method this semester. I thought I removed all those problems before posting the assignment, but these two slipped through. Sorry to anyone who has been working on these problems, and sorry to anyone whose access to the site was interrupted while I edited the assignment.

21-260: Correction to HW#4

Thanks, everyone who pointed out the repeated problem on this week's assignment. I've corrected the assignment page. The correct problems are 2.5.20, 2.5.25 and 7.1.22. I also corrected the quotation marks so they would come out correctly.

21-260: Week #4

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

21-260: Homework Solutions

The solutions to HW#1 will be made available in the section of the Blackboard site tomorrow at noon. Solutions to HW#2 will appear on the site Thursday at 5:00. Normally, in weeks unaffected by exam schedules, solutions will appear at 5:00 on the Thursday following the due date.

21-260: Existence and Uniqueness

I recently received an email asking for some clarification about today's lecture. I thought many of you might get something from my reply, so I'm posting it here:

You asked "Why do we need a rectangle for the second theorem?" The short answer is: "because nonlinear equations are not as nice as linear equations." But let me turn the question around: Why doesn't the first theorem require a rectangle?

If we start with the equation y' + p(t)*y = g(t), we rearrange things to get y' = g(t)-p(t)*y. We can apply the second theorem to this equation with f(t,y) = g(t)-p(t)*y.

If p and g are continuous on the interval (a,b), then f is continuous on the rectangle (a,b)x(-infty,+infty).

The partial derivative of f with respect to y is df/dy=-p(t). Since p is continuous on the interval (a,b), when we think of df/dy as a function of t and y, it is continuous on the rectangle (a,b)x(-infty,+infty).

So for linear equations, we can always choose a rectangle that is infinitely tall. There is one other issue, though. The theorem for linear equations says the domain of the solution is all of (a,b). An implication of this is that the solution cannot have a vertical asymptote before t=b. Why is this?

Well, a complete explanation is beyond the scope of this course, but it is basically because the growth of the slope y' only depends linearly on y, it can't grow quickly enough to get to +infty unless p(t) or g(t) has a discontinuity.

Here's a related problem: Consider the differential equation y'=y^p, where p is a constant greater than zero. This is a separable equation, and if you solve it, you will find that if p<=1, then the the solution is defined for all values of t, but if p>1, then the solutions have a vertical asymptote.

21-260: Week #3

The reading and homework assignments for Week #3 have been posted. You can follow the link from the Schedule page.

21-260: Office Hours

I neglected to mention my office hours in class this morning. Like last week, I'll be holding office hours tomorrow from 2:00-4:00. These will be my regular office hours for the semester. If you need to meet with me outside this time, let me know, and we make arrangements to do that.

21-260: Week #2

The reading and homework assignments for Week #2 have been posted. You can follow the link from the Schedule page.

21-260: Office Hours

I will be holding office hours tomorrow (Thursday) from 2:00-4:00pm. These may be my permanent office hours, but I'll let you know before long.

21-260: Blackboard Enrollment

I've heard from a few of you about problems accessing the Blackboard site for the course. It seems that only students from Lecture 1 were automatically enrolled. I've asked to have everyone from Lecture 2 added, and I'm told that should happen by the end of the day today. Don't worry, though, as there is really nothing on the Blackboard site yet, other than a link to the 21-260 Web Site.

UPDATE: It appears that all enrolled students have now been added to the Blackboard site. If you are still having problems accessing the site, let me know.

21-260: Waitlists

I've received some messages about waitlists for various sections. For what it's worth there is currently space in sections A and D. Sections B and C have one person each on their waitlists. Section E has no waitlist, but appears to be at it's maximum capacity.

Welcome to 21-260

Welcome to 21-260 Differential Equations. This I'll use this blog to post announcements about the course - when assignments are posted, when solutions become available, changes to office hours, and such. I'll also try to post links to anything I think would be relevant and interesting to you, as a student in the class. For more information about the class, you should check out the 21-260 Web Site.

21-260: Exam #3 Solutions

I've posted solutions to Exam #3 on the Blackboard site. There is an error in problem #4, as noted on the Blackboard site, but I wanted to get them posted before I can rescan the solutions on Monday.

21-260: Final Exam

The review page for the final exam has been posted. You can follow the link from the Schedule page.

21-260: Week #15

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

21-260: Week #14

The reading and homework assignments for Week #14 have been posted, as has the Exam #3 review page. You can follow the links from the Schedlue page.

21-260: Week #13

The reading and Homework assignments for Week #13 have been posted. You can follow the link from the Schedule page.

21-260: Week #12

The reading and homework assignments for Week #12 are posted. Follow the link from the Schedule page.

21-260: Week #11

The assignments for Week #11 have been posted. Follow the link from the Schedule page.

21-260: Exam #2

Most of you should have your Exam #2's back by now. The grade cutoffs for the second midterm are: A - 80, B - 70, C - 60, D - 40. If you took the makeup exam on Tuesday morning, I have your graded exam, you can get it before or after class tomorrow. I've made the grades available on the Blackboard site.

Week #8

The reading and homework assignments for Week #8 have been posted, and now linked from the schedule page, too. Since the assignment was not posted until now, I've removed one of the problems. You can find the assignment by following the link from the Schedule page.

21-260: Exam Date Changes

As I announced in class yesterday, I've had to move the second and third mid-term exams from their originally scheduled dates. The second mid-term, instead of being the Wednesday after spring break, will be the Friday after spring break, March 23. The third exam, instead of the Monday before spring carnival, will be the Friday after spring carnival, April 27.

I think the new dates will be generally preferable to the original dates, but in case they are not, let me tell you that the alternative would have been to give the exams on the scheduled days at 7:30 in the morning.

21-270: Week #7

The reading and homework assignments for Week #7 have been posted. You can follow the link from the Schedule page.

21-260: Exam #1

I returned Exam #1 during class yesterday. If you didn't get yours, you can pick it up from your TA during recitation today. The grade cutoffs for the exam are - A:85, B:75, C:65, D:50. These cutoffs are important for two reasons. First, it gives you an idea where you stand, and second, I use them to compute grade cutoffs for your cumulative averages.

Since the grade cutoffs for this exam are the same as for the homework assignments, the grade cutoffs for cumulative averages are the same, too - A:85, B:75, C:65, D:50. I compute the grade cutoffs for cumulative averages by averaging the grade cutoffs the same way I average your grades (i.e. the A cutoff for cumulative averages is the average of the A cutoffs for each assignment).

An important point to note is that, when computing your averages, the difference between, say, an 84 and 85 is only a 1% difference, not a whole letter-grade difference.

I will make your exam grades and cumulative averages available on the blackboard site.

21-260: EXCEL groups

My name is Sharanya Venkat and I will be your EXCEL Leader for
Differential Equations this year. EXCEL is a collaborative learning
program through Academic Development that focuses on providing extra
practice to students in groups of 5-6 people especially in Math and
Science courses. We will be going over key course concepts and doing
practice problems based on what you cover in lecture and your
homeworks.

EXCEL groups meet once a week for one hour, at a time that fits in
with your availability. Requests to join a study group can be made
through the Academic Development Office in Suite B5, Cyert Hall.

I hope to see you soon and good luck with the course!

21-260: Exam #1 Review

I've posted a review page for Exam #1. You can follow the link from the Schedule page.

Academic Development Workshop.

It's kind of short notice, but here is an announcement from Academic Development:

It's a new semester, are you ...

Facing new challenges and opportunities?
Worried that you’ll fall into the same habits that hurt you last semester?
Determined to have a more successful spring term?

If any of these apply to you then you could benefit from registering for one of the following dates of the "Getting Off on the Right Foot Workshop":

Tuesday, Feb. 7
4:30-6:00pm
Cyert B6-A

Register now...

21-260: Changes to Office Hours

I wanted to let you know about some updates to the schedule of office hours. Zhe Cheng has changed his hours to Tuesdays 2:30-4:30pm, Thursdays 3:30-4:30pm. Jacob Davis has moved his Tuesday office hour to Wednesday 7:00-8:00pm; his Thursday hours remain the same at 6:00-8:00pm.

I announced that my office hours would be Tuesday from 3:15-5:15pm, except on the first Tuesday of each month when a conflict would force me to move them later, to 6:30-8:00pm. This week only, as a result of another conflict, I'll have to move my office hours to Thursday, 2:00-4:00. Sorry for the confusion.

21-260: Week #4

The reading and homework assignments for Week #4 have been posted. You can follow the link from the Schedule page.

For this week's assignment, you may wish to use dfield to produce some of the slope fields (direction fields). If you are familiar with some other program for doing this, you may use that instead. (I know Maple has a facility for producing these diagrams.)

Morgan Stanley Assesses Prospects for US and Europe

Via Zero Hedge.

21-260: Office Hours

I announced my office hours at the end of class yesterday, but it may be that not everyone noticed. They will be Tuesdays from 3:15-5:15pm. They are also posted on the information page of the website, along with (most of) the TA's office hours.

21-260: Week #3

The reading and homework assignment for Week #3 has been posted. I haven't been able to get the WileyPlus assignment "assigned" from home, for some reason, so you won't be able to begin that until tomorrow. Also, there is still one problem for the written assignment that I need to write up.

21-260: Week #2

The reading and homework assignments for Week #2 have been posted. You can follow the link from the Schedule page.

Mathematics and Pasta

If you've ever been as frustrated as I've been by your inability to describe precisely the shape of your pasta, you will find this interesting.

Welcome to 21-260 Differential Equations

Welcome to Differential Equations for the Spring 2012 semester. I'll post information and announcements related to the course here, along with anything else I think you may find interesting.