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

Monday, August 31, 2009

21-260: Week #2

The reading and homework assignments for Week #2 have been posted. The assignment is linked from the schedule page.

Friday, August 28, 2009

21-260 Recitation Sections

I've had a number of people approach me regarding issues with their recitation section, and wait lists. The important thing for the semester is that you register for the recitation section you will be attending. I know many of you have said that your preferred section is full.

Most of the wait lists have dwindled down to only a few students. Here is what I would like you all to do in order to get everyone registered for the course:

  1. If you are registered for a section that you can not attend, switch your registration to a section that you can attend.

  2. If you can not register for a section that you can attend, put yourself on a wait list for a section that you can attend.

I understand that you may be reluctant to give up your spot in a section to put yourself on a wait list, but I don't foresee that any student will be unable to take the course due to enrollment limits. If it continues to be an issue, we'll work something out.

UPDATE: As I said above, the important thing is to register for the recitation you will be attending. It is better if you attend the lecture that corresponds to your recitations section, but if that is not possible, you can certainly attend the other lecture. They are, in principle, identical.

Thursday, August 27, 2009

The Father of Sinh

A student asked me about the origin of the hyperbolic functions in one of my recitations today. The Wikipedia article credits the Alsatian mathematician-physicist-philosopher-spelunker Johann Heinrich Lambert (who was apparently obsessed with equal-area map projections) with the invention of these functions, but his own article doesn't mention them at all. Maybe a disgruntled calculus student edited them out.

Google Timeline lists a reference back in 1631, by an English mathematician Richard Norwood, but that link is actually referring to trigonometric functions. The second reference in Timeline (A History of Mathematical Notations: Notations Mainly in Higher Mathematics by Florian Cajori) says that the hyperbolic functions were first used by Vincenzo Riccati in 1757, but he used the notation "Sh." for hyperbolic sine and "Ch." for hyperbolic cosine. Lambert is said to have invented the notation that we now use for these functions (sinh,cosh,tanh) in 1768. However, several other notations were used for these functions well into the 1900s.

So, we can take away from this that

(a) Wikipedia is not to be trusted, even in math;
(b) mathematical notation is all over the place; and
(c) inventing good notation for a concept will make you as famous as the people who invented the actual concept.

Minor correction for 21-260-A recitation 8/27

This morning, on problem 19, I broke up the derivative of t^r into two cases (r = 0 and r ≠ 0). I later figured out that this is actually unnecessary, since we were assuming that t > 0 in that problem and the others in that section of the homework. r*t^(r-1) = 0 when r = 0, and this is the correct derivative of a constant. (There would be a problem here if t were allowed to be 0, since we'd be raising 0 to a negative power, which is not allowed.)

So, you don't have to treat the case where r = 0 and r = 1 separately in that problem, which should make it a bit less tedious.

Also note that the equation in problem #1 was actually linear (I mistakenly listed it as nonlinear at the beginning of recitation). A linear differential equation may have terms that are not linear in t, as long as all terms are linear in y and its derivatives.

Monday, August 24, 2009

21-260: Welcome to 21-260

Welcome to 21-260 Differential Equations. As I mentioned in class this morning, there are several things your should be aware of for the course. First of all, the course website. This will be the source of much of your information about the course, via the schedule page and the link to this blog. Also, the Blackboard site, where you can look at your recorded grades, and find homework and exam solutions, and the Wiley-PLUS site, where you will complete online homework.

If you need to purchase a registration code for the Wiley-PLUS site, you can do that here. Once you have registered with the Wiley-PLUS syste, you can access the course materials via this link.

UPDATE: The course-specific URL you need to register/access the Wiley-PLUS page is