Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.
Tuesday, December 4, 2012
Sunday, December 2, 2012
Wednesday, November 28, 2012
Sunday, November 25, 2012
Saturday, November 10, 2012
Tuesday, November 6, 2012
Saturday, October 27, 2012
Tuesday, October 23, 2012
Monday, October 22, 2012
Friday, October 19, 2012
Saturday, October 13, 2012
Saturday, October 6, 2012
Sunday, September 30, 2012
Wednesday, September 26, 2012
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
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.
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.
Friday, September 21, 2012
Monday, September 17, 2012
Sunday, September 16, 2012
Friday, September 14, 2012
Tuesday, September 11, 2012
Monday, September 10, 2012
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
Wednesday, September 5, 2012
Saturday, September 1, 2012
Wednesday, August 29, 2012
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.
Tuesday, August 28, 2012
Monday, August 27, 2012
Saturday, May 5, 2012
Friday, May 4, 2012
Monday, April 30, 2012
Friday, April 20, 2012
Friday, April 13, 2012
Friday, April 6, 2012
Friday, March 30, 2012
Thursday, March 29, 2012
Monday, March 5, 2012
Thursday, March 1, 2012
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
Thursday, February 23, 2012
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.
Thursday, February 9, 2012
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
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
Tuesday, February 7, 2012
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
Monday, February 6, 2012
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.
Friday, February 3, 2012
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
Via Zero Hedge.
Sunday, January 29, 2012
Sunday, January 22, 2012
Thursday, January 19, 2012
Wednesday, January 18, 2012
- academic development
- carnegie mellon
- engines of our ingenuity
- enigma machine
- mad river glen
- math club
- mathematical constants
- office hours
- spring break
- square dancing
- study break
- urban decay
- zero tolerance
- ► October (6)
- 21-260: Week #6
- 21-260: Week #5
- 21-260: Study Break
- 21-260: Exam Strategy
- Chris Potter's office hours
- 21-260: Exam Odds and Ends
- 21-260: Week #3 Homework Solutions
- 21-260: Week #4 WileyPLUS Assignment
- 21-260: Correction to HW#4
- 21-260: Week #4
- 21-260: Homework Solutions
- 21-260: Existence and Uniqueness
- 21-260: Week #3
- 21-260: Office Hours
- 21-260: Week #2
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