Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.
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
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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)