Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.
Tuesday, December 4, 2012
21260: Final Exam
Sunday, December 2, 2012
21260: Week #15
Wednesday, November 28, 2012
Sunday, November 25, 2012
21260: Week #14
Saturday, November 10, 2012
21260: Week #12
Tuesday, November 6, 2012
21260: Week #11
Saturday, October 27, 2012
21260: Week #10
Tuesday, October 23, 2012
21260: Week #8 Solutions
Monday, October 22, 2012
21260: Exam #2 Review
Friday, October 19, 2012
Exam #2 Review Problems
Saturday, October 13, 2012
21260: Week #8
Saturday, October 6, 2012
21260: Week #7
Sunday, September 30, 2012
21260: Week #6
Wednesday, September 26, 2012
21260: 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.
Monday, September 24, 2012
21260: Exam Strategy
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 2025% of the exam to be pretty straightforward, and another 2025% 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
Mon 46pm
Tue 24pm
Wed (none)
Thu 45pm
21260: Exam Odds and Ends
As announced in class today, our first midterm is this Wednesday from 7:308:20 in UC McConomy. There will be no class on Wednesday. I will hold a review session tonight from 6:308:00 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.
Friday, September 21, 2012
21260: Week #3 Homework Solutions
Monday, September 17, 2012
21260: Week #4 WileyPLUS Assignment
Sunday, September 16, 2012
21260: Correction to HW#4
Friday, September 14, 2012
21260: Week #4
Tuesday, September 11, 2012
21260: Homework Solutions
Monday, September 10, 2012
21260: Existence and Uniqueness
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.
Saturday, September 8, 2012
21260: Week #3
Wednesday, September 5, 2012
21260: Office Hours
Saturday, September 1, 2012
21260: Week #2
Wednesday, August 29, 2012
21260: Office Hours
21260: 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 21260 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.
Tuesday, August 28, 2012
21260: Waitlists
Monday, August 27, 2012
Welcome to 21260
Saturday, May 5, 2012
21260: Exam #3 Solutions
Friday, May 4, 2012
21260: Final Exam
Monday, April 30, 2012
21260: Week #15
Friday, April 20, 2012
21260: Week #14
Friday, April 13, 2012
21260: Week #13
Friday, April 6, 2012
21260: Week #12
Friday, March 30, 2012
21260: Week #11
Thursday, March 29, 2012
21260: Exam #2
Monday, March 5, 2012
Thursday, March 1, 2012
21260: Exam Date Changes
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.
Saturday, February 25, 2012
21270: Week #7
Thursday, February 23, 2012
21260: Exam #1
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 lettergrade difference.
I will make your exam grades and cumulative averages available on the blackboard site.
Thursday, February 9, 2012
21260: EXCEL groups
Differential Equations this year. EXCEL is a collaborative learning
program through Academic Development that focuses on providing extra
practice to students in groups of 56 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!
Wednesday, February 8, 2012
21260: Exam #1 Review
Tuesday, February 7, 2012
Academic Development Workshop.
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
4:306:00pm
Cyert B6A
Register now...
Monday, February 6, 2012
21260: Changes to Office Hours
I announced that my office hours would be Tuesday from 3:155:15pm, except on the first Tuesday of each month when a conflict would force me to move them later, to 6:308:00pm. This week only, as a result of another conflict, I'll have to move my office hours to Thursday, 2:004:00. Sorry for the confusion.
Friday, February 3, 2012
21260: Week #4
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.)
Tuesday, January 31, 2012
21260: Office Hours
Sunday, January 29, 2012
21260: Week #3
Sunday, January 22, 2012
21260: Week #2
Thursday, January 19, 2012
Mathematics and Pasta
Wednesday, January 18, 2012
Welcome to 21260 Differential Equations
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Blog Archive

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2012
(54)

►
September
(15)
 21260: Week #6
 21260: Week #5
 21260: Study Break
 21260: Exam Strategy
 Chris Potter's office hours
 21260: Exam Odds and Ends
 21260: Week #3 Homework Solutions
 21260: Week #4 WileyPLUS Assignment
 21260: Correction to HW#4
 21260: Week #4
 21260: Homework Solutions
 21260: Existence and Uniqueness
 21260: Week #3
 21260: Office Hours
 21260: Week #2

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September
(15)