Greetings. Welcome to Math 20E, Lecture B, with Kate Okikiolu. I am your Dedicated Servant Teaching Assistant, Chris Tiee. This is just an additional supplements page; see the Main Course Webpage for all official information regarding class.
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Instructor: Kate Okikiolu
Office: Applied Physics and Math (AP&M) 7426
Email: okikiolu@math.ucsd.edu
Textbook: Vector Calculus, 5th Edition by Jerrold E. Marsden and Anthony J. Tromba
I also recommend: Div, Grad, Curl and All That: An Informal Introduction to Vector Calculus by Harry Schey. It helps you sort out what vector integration means. This text is completely optional, however. Also check out Schaum's Outline on Vector Analysis. Lots of solved problems in there.
TA: Chris Tiee
Office: AP&M 2301
Email: c tiee at math dawt ucsd dot edu (please replace at with @, dot and dawt with . ; this is an anti-spam measure.)
Office Hours: Tu 2-4, W 1-2, F 1-2, and by appointment. (I had earlier said in section I had a Monday office hour; in case you haven't heard, I've changed it to Friday.)
Discussion Times & Location:
B03: 4:00-4:50pm
B04: 5:00-5:50pm
B05: 6:00-6:50pm
B06: 7:00-7:50pm
All sections are in Solis 109.
Sat 3/18/06 - The Plan for Next Week, Midterm 2 Regrades, Misconceptions You May Have About Me, and Final advice.
I'll hold office hours on Tuesday from 1-3pm. I have my own final exam to take at 3 then, so please try to make it early so as to not keep me overtime. I will also be around in my office on Monday, so if you cannot make 1-3 Tuesday or you would prefer to stop by sooner, send me an email on Mon. morning before you come; I will be in a meeting with a professor on Monday from 2-3 so keep that in mind.
For Midterm 2, most tests are likely to not be regraded, because most answers were not clear on the reasons why one could reparameterize the curve. I made it clear in section that you had to be clear about that. After all, if the field was not conservative, you would get a different answer for parameterizing it as a straight line (just look at problem 1, for example). This is another crucial note: Just because the exam hints that the field is conservative does not mean it is; you must still show it. Yes, I know you are going to say, "What is the point? Isn't that a waste of ink?" We provided the hint in order to perhaps jog your memory at what kind of field you might be looking for, not as a shortcut for you to sigh in relief "Oh ok, they did half the problem for us, good."
Three additional remarks are in order before you start firing up your email clients.
First, if you still have a problem with the grading of #2, please take it up with Aaron (be aware that his spine is in a better condition than mine).
Second, speaking of my spine:
I may be a nice guy; I may want to be your friend; I may be easygoing; and I may poke fun at TAs or profs who like to rule over their students with an iron fist. But none of these facts are a substitute for mathematical correctness, which is what you will be tested on. I say in advance for the final that you will not get away with incorrect reasoning (without losing points). (Be aware that I will be done with my Complex Analysis final by the time I get to grading your exams, I have no vacations planned for Spring Break, the Internet will be disabled at my place from 3/23-3/29, and I'm one of those kinds of people who are perfectly capable of having fun without the assistance of alcohol. So expect your exams to have my undivided attention). Bridges will not hold and buildings will not stand because Theorem 22.9.16 says so, the Magic Fairy says so, or Chris says that they will. And if they stand now due to your good luck ("I got the right answer, so what if everything else I did was wrong?"), who knows what's going to happen with the next one you build? I am sorry, but what you were told in elementary and high school about how "In math, the only thing that matters is the answer, and if it is right, it is right," no longer applies. This is not an infection of wishy-washy relativism into something supposedly "rigid" such as mathematics, but rather an expression of the fact that concrete results in the real world are merely the endings of very long, complicated stories, in which the middle parts do matter. That is to say, the "flow" of life does not represent a conservative vector field; The Fundamental Theorem of Calculus for Line Integrals does not apply, and results are dependent on the path you take to get there. It ain't as simple as endpoint minus startpoint. On the flip side, absolute perfection is not that easy to achieve. So as a compromise, there's this thing called partial credit...
Finally, since philosophical remarks probably have made you weary at this point, I'll let you in on perhaps the most practical advice. If the problem gets regraded for substantial partial credit, the exam will end up not being curved. Witness, for example, what happened when die Dreikäsehochs quoted the precedent of Håkan v. Math 20E Winter '05 Midterm 1. This plan may very well have backfired, because it raised the average considerably. This means Midterm 1 will not be curved unless you want it to work against you (technically speaking it may work against you, in the sense that, since we curve everything at the end of the class, it will give you less wiggle room for the final. I say this because I do not want to make false promises; I've had more than one upset student in previous quarters come back to me "But you said I was sure to get this grade, but I didnt!"). Anyway, you can give thanks den Dreikäsehochs for that (yes, I typed this as an excuse to use emphasis within emphasized text, to use the letters å and ä, and to use the dative case in German). I've set a new precedent with this solution for problem 4. If problem (4a) appears on the final again, I hereby give you permission to memorize and repeat this proof (but not just quote it, as in "Oh a supplement on Chris's website..." or something along those lines) for full credit. Maybe you would prefer to compute a curl in full after all.
My advice for the final, or generally on a test any math class then is: Use your good judgement, and don't count on technicality to save you. (Again, still giving evidence I'm not quite over having to do that Midterm 1 regrade, I should say that if you want to get technical, note that quoting an answer on a midterm given in a previous quarter is technically an offense that can get you expelled. This is the first place where I would start getting technical about.) Remember, the point is to try your best. If that means you may have to waste ink, then yes, waste ink. Waste paper. And <<insert deity here>> forbid, waste time, because if some extra words will make it more clear to the grader that you at least have some idea of what you are talking about, it will make all our lives easier (for example, it will make our grading go faster, make it more likely you will get a favorable number of points on that problem, and save you the trouble of having to come and argue why your problem was graded the way it was graded). HOWEVER, purposely filling your paper with meaningless junk in effort to make my remark here backfire is not going to work. Finally, if you haven't looked already... Supplements.
Mon 3/13/06
The second midterms have been graded. Come during office hours to pick them up, or to section. Here is the score distribution.
which amounts to a mean of 65, median of 65, and standard deviation of 22,7.
Pop Quiz! Match the following varieties of pasta to their respective parameterizations:
Note that generally s and t are the parameters, and other letters such as k, α, β, γ are constants.
Fri 2/24/06
Here is a supplement which summarizes the various integrals we've developed, and step-by-step procedures for solving them (including finding parameterizations of surfaces. Note also it says midterm 2 preparation as it was originally intended for a midterm 2 prep for last year's 20E class. But it serves well as a general overview, and it will most likely work as a good prep for our midterm 2, too, though I can't guarantee that). Also, please take a look at Why gradients don't have curl as it has an overview of calculating an "antigradient" from a vector field. This can be very useful in calculating line integrals that are known to be independent of path (in fact, if you can calculate an antigradient, it follows immediately that the line integral is in fact independent of path). [These are the same supplements I mentioned last week and the week before. I'm inserting them here again for the benefit of those who have an attention span as short as mine.]
Also, regarding Section 7.5 on the homework: these problems will not be graded, as they were just barely covered in lecture. However, do get some practice, and work on these problems as if they were part of next week's homework. Come to office hours next week if you have questions on this; the concepts in this section figure pretty heavily in 7.6 and onward, so be sure to know it well. Section 7.5 is also summarized in the supplement.
Thurs 2/16/06
Midterms have been regraded and some handed back in section. If you didn't pick yours up, I will have them in my office tomorrow at 1-2 PM. Also, you can get them in the normal lecture time tomorrow. Here is the new score distribution:
which amounts to the stats 77 mean, 81 median, and standard deviation 17. Finally, here's a nice mock solution to problem 4a. Be sure to memorize the solution for the final! =). I've also included a new supplement which gives a big picture overview of multiple integration.
Fri 2/10/06
I handed back graded midterms in section. Needless to say, a fraction of the students were dissatisfied (1/1 is a fraction, isn't it?). There is a rather big grading issue. If you think this affects you, return the test, even if you left section, and even if I had said I won't regrade a certain problem (especially sections B03 and B04; this is all due to revelation in yesterday's B05 section), in class on Monday (it was announced in class on Friday).
The issue at hand is that an old midterm solution had an answer that was acceptable to another TA. I decided as a good compromise, it is fair to return most, but not all, of the credit. I say "most" because those who calculated it as intended (of which there were many!) do deserve something for their work, and also I do not want to set a "bad precedent." To paraphrase certain recent Supreme Court appointees, I am not bound to the precedent set by Håkan v. 20E Winter 05 Midterm 1. (Yes, I wrote this just to have an excuse to use the letter å). So please note this is a one-shot solution; I'm only letting you get away with it this time. So now I shall give an explicit, yes, very explicit statement for future reference:
"But ____'s solution from an exam ____ quarter said that answer was acceptable!" will no longer be a valid excuse for regrade! (that's what it always should be!). This is college, so let's not be acting like dreikäsehochs!
On the flip side, perhaps there are some things that Håkan graded in a manner more harshly than I would. TA's have their individual style. Things like curves adjust for this kind of variation. In my case, the average was high enough even without any regrades (75, by the way). You should try taking a section with one of my office mates some time, Mr. 30%-is-average-and-50%-is-really-darn-good. Finally, let me say that this is not such a big deal in the grand scheme of things. Learn to relax!
Fri 2/03/06
Webpage is (finally) up. Check here regularly for updates. I put up some supplements.
Thurs 1/12/06
First discussion. Hi!
We will be covering most of the textbook, skipping parts of Chapter 3 on min/max problems, and the last section in the book... although that stuff is really cool. Chapters 1 and 2 are mostly review.
Personal Philosophy of the 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).
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. People applying vector calculus get along fine using n-dimensional calculus.
Homework will be assigned each week. Though it is worth only 10% of your grade, you should do it, because it's good practice for the midterm. It will be due the following week in Thursday section (preferable, to keep things organized) or in the homework drop box on the second floor, down the hall from my office, AP&M 2301, by 4pm on Friday, for your convenience. There are two boxes on the wall; mine is the right box, first column, and second slot from the top (you'll see 20E and my name on it).
I encourage people to work together on homeworks, and definitely come to office hours to discuss these problems. 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 n times on account of that, n 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.
Finally, a frequent complaint the last time I did 20E was that I would "never finish" a problem, but rather reduce many problems to things that can be done using Math 20B. I would often joke "To finish this off, bribe your friends in 20B." I don't do these in section simply because they can be tedious, time-consuming, and beside the point. Plus I simply won't get through enough material if I dwell on a complete, shiny solution. If you would really like to see a problem worked out in detail as such (it still is good practice), please come to my office instead. You will receive the bulk of the credit for exam problems for proper setup (this is essentially the point of the class, as this is what requires the conceptual understanding), not final answers.
Why gradients don't have curl. If you are interested in some of the intuition behind the fact that the curl of a gradient of a function is zero, this will hopefully be helpful.
Old homework solution, which includes several pictures of parameterized paths and vector fields (including a picture of the gradient vector field given in 4.3, #20). This is actually a solution to a homework set in the class from Winter 05; you may read over it for practice but please be aware that it is not the the same assignment as our Homework 4. Please beware that it is 473K in size so, unless you have a fast connection, be prepared for a wait. Note: solutions to the actual homeworks are on the Main Course Webpage.
A Guide to Coordinate Changes and Parametrizations, which tries to capture the essential procedures and "rules of thumb" in all our different varieties of integral (line, surface, 2D, 3D, plain ol', etc). It says midterm 2 preparation as it was originally intended to prepare the students for midterm 2 in last year's 20E class. But it serves well as a general overview, and it will most likely work as a good prep for our midterm 2, too, though I can't guarantee that.
Questions? Comments? Complaints? Send email to ctiee@ucsd.edu. This page does not represent the views of the numerous institutions I am affiliated with.
