Math 20E Lecture A, Discussions Page

[This is not the Math 20E Spring 05 page. For that, click here.]

Administrativa

Greetings. Welcome to Math 20E, Lecture A, with Stephen Pav. I am your Dedicated Servant Teaching Assistant, Chris Tiee, TA'ing sections A02 at 9am, A03 at 10am, A04 at 11am, and A06 at 1pm, all on Thursday. Please note, however, that two sections (A01, 8am and A05, 12 pm) were cancelled, at least according to the math department. The irksome thing is that it doesn't show up on the registrar's page and none of the few but not zero people in these sections were notified of this. No TA is assigned for those sections (originally there were supposed to be two TAs for this class). So if you are enrolled in those sections, please enroll in the others (go to the math Add/Drop office, AP&M 2402A).

Aside from those cancelled sections, you may attend any, all, or none of the sections, regardless of the one you are enrolled in. However, do put your section number (A02-A04 or A06) on your homework, it makes it easier for me to keep track of things, and also less likely that I may lose your homework (and I am prone to doing things like that!).

Here's some contact info (repeated from my main page for those who have an aversion to clicking the "back" button...).

Office: Applied Physics and Math, 6349A
Email: ctiee@ucsd.edu

Office Hours (Winter 2005):

Tuesday 2pm-4pm
Wednesday 1pm-2pm
Friday 1pm-2pm

Extra Office Hours for Midterm 1

Friday 1/28 4pm-6pm

Skip to Solutions

Teaching Philosophy and Goals of Class

In effort to bore the reader as much as possible, I shall state my feelings about this class. First off, vector calculus is an extremely cool, interesting, and even beautiful subject. I'm not kidding... You may think I am crazy (a true fact, but for entirely different reasons). Many of the laws of nature can be described by in terms of vector fields, their derivatives, and integrals. Consequently, this should be very useful to those of you who are planning to be engineers or physicists (and more recently, computer game programmers). There are also many deep connections of this stuff to other branches of mathematics, but unfortunately, if you're a budding math student, you are not likely to see and understand those connections it until graduate school, and consequently you will be, paradoxically, much more likely than your physicist and engineer peers to forget the material in this course after you're done (try taking differential geometry, the Math 150 series, as soon as possible).



An Inverse Square Vector Field (e.g. Gravity).

My goal is to try to get you to get a feel for all this stuff, so that you don't feel like you're just pushing around symbols. Vector calculus has a somewhat undeserved reputation for being "hard." I'm not entirely sure how it gets this reputation, but I suspect it has to do with the intimidating nature of the new notations one encounters such as multiple integrals (actually the integral sign is one of my favorites; I've always been fond of cool notation), and that it involves 3-D stuff which is harder to visualize. While it's useful to have the ability to actually visualize these abstract 3-D objects and rotate them in their heads and so forth, it's not absolutely necessary to do well in this course. Also it is a skill you can develop; just because you can't do it now doesn't mean you can't do it ever. Getting an intuitive idea of this stuff is not necessarily the same as having elite visualization skills (iREET ViSu@|_][Z4ti0n SkiLLz). After all, some of these things generalize to n-dimensional space for n > 3, in which these things are impossible to visualize. Yet people get along fine using n-dimensional calculus in daily life.

Homework

The impatient reader, I'm sure, has been itching to get to this section. My own official policy on homework, due dates, and so forth is better late than never. If you have doubts as to whether you'll be able to get an assignment in on time (say, you're coming down with a dreadful flu of some sort), try to send me email in advance; more often than than not, if you have some kind of reasonable explanation, I'll take it. That holds even if you come to me afterward. If your homework indicates you've made an honest effort and spent some real time doing it--ultimately this is what counts, come exam time--it is surely a pity to just have to throw it away. So please do not just give up on a homework assignment because you think you won't get credit for it.

This is college, not prison, so I'm not here to be a watchdog on your discipline (within the bounds of academic policy, of course, i.e. no cheating!). After all, I don't have a great deal of that, either. Nevertheless, I do not want to encourage excessive dilatory behavior, and if it becomes a habit, or it's really, really late (namely after the solutions come out) I won't be so nice. There is in fact an issue of fairness that I don't want to get into right now, and excessive shuttling of homework back and forth to the grader will be rather irksome. Finally (won't he shut up already?) homeworks are preparation for exams, so keeping up to date is ultimately to your own benefit.

I've set up a homework drop box by my offfice AP&M 6349, for your convenience. There are two boxes on the wall; mine is the left box, second column, and second slot from the bottom (you'll see 20E and my name on it). Please drop your homework in there by 5pm on Thursdays (3 hours after the end of the last discussion, A06). I encourage people to work together on homeworks, and definitely come to office hours to discuss these problems (I don't have any office-mates, so I get lonely). While I will try to do problems in section, as the course progresses to harder and more important concepts, I will be spending more time talking about these things. So please make use of office hours; importantly, don't be shy (I have been heartbroken twice on account of that, two times too many).  Don't just "copy" homework or take my solutions and run with them--the goal, remember, is to try to understand what's going on. After all, I can't be there to take your midterms and final for you. Finally, I refer you to my Links Page for other sources of help.

Due Dates and Solutions (See this page for assignment)

Now that you know that your TA is very long-winded, we'll get to what you're really here for: homework solutions. For each assignment I shall strive to have them out by Monday following discussion so you will have the reference ready when you get your homework back. You are welcome to discuss the solutions with me as well, in office hours or over email. Also please point out any errors you find--this is, in fact, possible; nobody's perfect. They will make excellent midterm study material. I shall try to include commentary from what I did in section, but this will tend to make the solutions very long. So unfortunately the "quality" of homework solutions will vary according to my own schedule.

Solutions are in .pdf form. If you use Mac OS X, the included Preview application will view these files automatically after downloading. For other platforms you need Adobe Acrobat Reader, obtainable by clicking the cute image below.



Homework 1, due 1/13/05. Solution.
Homework 2, due 1/13/05.

Solutions updated (1/27/05 11pm). Graphs are easier to see.
Graphics Intensive Solution (300K, dialup users beware).
Even Problems Only, with fewer graphics (63K)

Homework 3, due 1/20/05

Solutions updated (1/29/05 9pm). Please re-download, since even though I updated, my web-editing software made a copy and kept uploading the old solution anyway. Annoying, I know.
Solution (122K)

Homework 4, due 1/27/05

Complete Solution. (472K) (Updated 9pm 1/30/05) Graphics intensive and includes several pretty plots of vector fields.. It is 13 pages long, beware. I heard ye wail for solutions, well solutions ye get, till they come out your nostrils! =)

Here's an important and hopefully-helpful-for-midterm conceptual discussion on why gradient fields can't have curl. It basically explains a few nagging questions one gets from looking at various "exam prep" questions (268K pdf file)

Last but not least. Good luck on the exam! I'll see you there tomorrow.

Comments about the midterm (2/1/05)

I've finished grading the midterms. The scores were relatively high (mean 86, median 88), and so I was generally happy. Recall that there is a guarantee that "the curve" will not work against you, that is, the score required to get an A, B, C, etc. is guaranteed not to go higher than 90, 80, 70, etc. respectively. So please do not stress out over this. One thing, however, that almost everybody missed 6c, the question on whether the vector field F is the gradient of some scalar field, despite the fact that almost everybody computed the curl correctly in part 6b, to be nonzero (ironically, one person incorrectly computated of a curl to be zero, and also "missed" 6c by answering yes, for the correct reason, and hence got full credit for that part for consistency!). I believe this is because of the wording about "continuous partials" etc. that may have thrown people off to think that it was a question for general F. But still, to be the gradient of something, besides having continuous partials, it also must have curl zero. This is the point of what I explained this in great detail here (and some would say, too much detail!) but I am afraid that it has reached only a very small audience.

Finally a general homework-related issue that was brought up in a conversation: another TA I know asked his section "How long do you spend on a homework problem before you give up on it?" "Raise your hand if it's less than 5 minutes?" Most people raised their hands. This is amazing, since, people are usually afraid to admit even the most innocuous things; getting people to raise their hands in class is far more taxing than calculating the homology of RP2 with coefficients in Z. People are quite proud of their impatience, it seems ("The boy has no patience. I cannot train him." -- Yoda). Now I'm not trying to imply you are impatient, but rather to let you know that if you seek to learn anything in life you have got to have more patience than that.

The midterm will be returned along with uncollected homework next week in section.

Homework 5, due 2/3/05

Partial Solution (Updated 11pm 2/14/05).

Midterm Prep (Updated 6:15 pm, 2/27/05)

Here I have something that will help people to try to see what is going on. There are so many weird concepts and a mishmash of different techniques that it is easy to get lost. There are some illustrative problems in it.. Focus on the "easier to evaluate" problems and please do not tear your hair out in frustration over the hard-to-evaluate ones because it is more important that you get the concept of setting these things up than actually evaluating the things. On the midterm, the integrals should be easy to compute; otherwise you will likely get a "set up but do not evaluate" problem on the midterm. Even if not, I'm the one grading it, so, if some hard-to-evaluate problem comes up, you have my assurance that you will receive the bulk of the points for setup.

Midterm Prep (complete)

Also please go to the professor's web site for the class (link at top) as he has answers for the exam prep sheet up.