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:
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.
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:
If you are registered for a section that you can not attend, switch your registration to a section that you can attend.
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.
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.
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 http://edugen.wiley.com/edugen/class/cls128224/
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 http://edugen.wiley.com/edugen/class/cls128224/
Tuesday, July 28, 2009
An Interview with James Stewart
The MAA has posted an interesting interview with James Stewart, the author of the calculus textbook we use here at Carnegie Mellon. Included: his passion for music, and his remarkable home, "Integral House."
Friday, May 22, 2009
21-270: Final Wrapup
Well, the final grades for the course have been turned in. You can look at your exam grade in the Blackboard site, which will remain up for a little while longer. I'm not sure how long. Here are the final statistics for the course, including the cutoffs for final averages.
Have a great summer!
Have a great summer!
Monday, May 4, 2009
21-270: Final Exam
The Final Exam will be given on Thursday morning, from 8:30-11:30am. The exam will be in McConomy Auditorium. I will try to schedule a reveiw session for Wednesday afternoon, and I'll post information about it here when I know more.
I've posted a review page with some information about the final. Note that the Final will be cumulative. You should be sure to review the study problems from the first three exams, as well as your homework and exams.
UPDATE: Solutions to Exam #2 are now available from the blackboard site.
UPDATE: I've posted the formula sheet for the final exam on the blackboard site and the review page.
UPDATE: Solutions to most of Exam #3 are now available on the blackboard site.
UPDATE: Here are the current Statistics for the course.
UPDATE: Grade cutoffs have been corrected on the Statistics page.
I've posted a review page with some information about the final. Note that the Final will be cumulative. You should be sure to review the study problems from the first three exams, as well as your homework and exams.
UPDATE: Solutions to Exam #2 are now available from the blackboard site.
UPDATE: I've posted the formula sheet for the final exam on the blackboard site and the review page.
UPDATE: Solutions to most of Exam #3 are now available on the blackboard site.
UPDATE: Here are the current Statistics for the course.
UPDATE: Grade cutoffs have been corrected on the Statistics page.
Friday, April 17, 2009
Who are the Monsters?
Recently I received an email from the AAUP (American Association of University Professors), as I do from time to time. The text of the email is reproduced here. It begins as follows
The author, AAUP President Cary Nelson, goes on to say "What I learned in 1964 was to value the power of silent, nonviolent witness." Then Nelson gets to his main point: the reaction of various colleges to speaking engagements by Ward Churchill and William Ayers, who, Nelson would have us believe, are really quite nice people once you get to know them. They certainly are not without their controversies. But let's assume they simply follow Oscar Wilde's dictum: "The only thing worse than being talked about is not being talked about."
Nelson recounts several situations where speeches by Ayers, Churchill, and Richard Dawkins have been cancelled due to threat of financial losses or physical violence.
So there you have it. Controversial "right-wing" speakers are afforded an oportunity to air their views on campus, while speakers from the left are driven out by threats and intimidation.
But things are not so neat and tidy. There is a reason that Nelson pulls his initial example from 1964. Things aren't like that anymore, as Tom Tancredo, an opponent of "illegal" immigration, discovered at a recent speech at UNC. Tancredo's speech on immigtration was disrupted by protestors, and ultimately cancelled when protestors broke a window of the room where Tancredo was speaking. You can watch the video here. Now suppose that Tancredo is a real monster, not a "false monster" like Ayers or Churchill. Why is he not accorded the same opportunity as a Nazi?
What does the AAUP have to say about Tancredo's experience at UNC?
Violence is not speach. And once violence is injected into politics, it is very difficult to remove.
Over 40 years ago, when I was still an undergraduate at Antioch College, the student government sent out a large number of letters to controversial or accomplished Americans and invited them to talk on campus. One who accepted was George Lincoln Rockwell, head of the American Nazi Party...
...[T]he 500 students and faculty in the auditorium that day in 1964 ... sat in absolute silence throughout the talk. When the question period came ... everyone rose and exited, again in silence. So Rockwell began to curse us all. Still no one reacted. Eventually he gave up and left.
The author, AAUP President Cary Nelson, goes on to say "What I learned in 1964 was to value the power of silent, nonviolent witness." Then Nelson gets to his main point: the reaction of various colleges to speaking engagements by Ward Churchill and William Ayers, who, Nelson would have us believe, are really quite nice people once you get to know them. They certainly are not without their controversies. But let's assume they simply follow Oscar Wilde's dictum: "The only thing worse than being talked about is not being talked about."
Nelson recounts several situations where speeches by Ayers, Churchill, and Richard Dawkins have been cancelled due to threat of financial losses or physical violence.
So there you have it. Controversial "right-wing" speakers are afforded an oportunity to air their views on campus, while speakers from the left are driven out by threats and intimidation.
But things are not so neat and tidy. There is a reason that Nelson pulls his initial example from 1964. Things aren't like that anymore, as Tom Tancredo, an opponent of "illegal" immigration, discovered at a recent speech at UNC. Tancredo's speech on immigtration was disrupted by protestors, and ultimately cancelled when protestors broke a window of the room where Tancredo was speaking. You can watch the video here. Now suppose that Tancredo is a real monster, not a "false monster" like Ayers or Churchill. Why is he not accorded the same opportunity as a Nazi?
What does the AAUP have to say about Tancredo's experience at UNC?
Search: tancredo
Found: Nothing!
Violence is not speach. And once violence is injected into politics, it is very difficult to remove.
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