Without any digressions, took 35 minute to cover this, leaving 10 minutes for going over the syllabus and 5 for starting a little late. When covering distance in n-dimensions, it would be better to first compute the distance for the origin O to P and also to label the points as O and P in the 2D and 3D examples.
Final exam schedule request due to Aaron.
Did not get to the derivation of the dot product formula on page 6. Also hit the dot product 40 minutes in. Next time cut something to so I will have 12.5-15 minutes for the dot product. For example, position vectors and some of the properties of vector operations.
This lecture is way too long. The first time through, I had to skip parameterizing the line L entirely! The second time, I skipped the discussion of regression and got through more, but it was still tight.
In both sections, got through the plane example but not the triple product or anything after that.
In both sections, got through everything with essentially no time to spare.
Assign exam rooms based on current enrollments (Nathan)
Got through the proof that h^2 has limit 0 at 0 in both sections, but not h^2 + 2h. In the 8am, had no time to spare, in the 9am had about 3 minutes. In both cases, started limits between 20 and 25 minutes in (closer to 20, I think). The discussion of quadric surfaces types was done quickly by showing the Interactive Gallery and referring them to the upcoming discussion section on this topic.
Exam 1 draft due (Nathan and Sue)
In both sections, got up to the top of page 5, just before "rules for limits" with time enough to do the limit pictures Mathematica notebook and tell the sad story of the Sleipner A.
The description of HW 7 is "This HW covers questions on limits (14.2), but not continuity" but the very first problem (and only that problem) involves continuity! Move this problem to the next assignment in future years.
Exam 1 to printer.
I was under the weather a bit, and in that context the lecture seemed a bit long. I did get through page 6 in both sections, but I really had to keep an eye on the clock and push it to make this happen.
The first lecture went poorly because of computer glitches. In the second lecture, I got through everything except the proof of the first theorem at the bottom of page 5. I had to keep the pace up for that to happen, however, so as usual it would be nicer if the lecture was shorter.
In the first lecture, got through page 5 only by working at a demandingly quick pace. In the second lecture, ran out of time halfway through page 6. Overall, there's a lot to write out in this lecture, and overall the lecture is a bit long. I suspect the whole derivation of the Chain Rule is too messy for them to get much out of; on the other hand, it is a nice of example of using linear approximation theorically, which will occurs frequently in these lectures. Perhaps one should derive the single-variable chain rule and then just talk about what happens for two variables in a more heuristic fashion.
HW 10 should make clear in the intro that some of the problems, namely those involving the Chain Rule for partial derivatives, depend on the very beginning of the next lecture.
This lecture is a nice length; even though I expanded the first part slightly to deal with leftover material from the previous lecture, I was able to get through it all without working too hard.
This lecture is a nice length and I was able to get through it all without working too hard.
In the first hour, I got through the top of page 6 fine and then tried to cram the last example into 3 minutes. In the second hour, I skipped the top of page 5 and so had more like 5-6 minutes for the last example, which was still too little to cover it completely. Also, in both sections, I forgot about the Mathematica visualization.
This lecture is a good length. In the first section, I even got through a reasonably complete discussion of why the local max is the absolute max. In the second section, I didn't have time for the absolute max discussion, but I didn't have everything (including the contour plot) up beforehand as I was answering questions during the break.
HW 15 says: "This HW covers Lagrange multipliers, but not multiple constraints (14.8)" but in fact the final problem has two constraints. This should be resolved somehow.
This lecture is ok, I got though everything though I wished it was a bit shorter.
In detail, this is §13.1, the first subsection of §13.2 (through page 849), the first subsection of §13.3 on arc length (through page 855.5), and §13.4 through page 863.
This lecture is actually slightly short for once. I padded it out with a discussion of what the integral of x over the 1/4 circle C is means in terms of an area, and also said that "ds" is called the "arc-length element", which is at the beginning of the next notes. Should have included that the integral of 1 is the length.
Exam 2 draft due (Sue and James)
This lecture is a good length. It was 3-4 minutes short for the first hour and exactly right for the second. In the first lecture, I padded it out by extending the last example with a parameterization of the same curve going the opposite direction.
Should learn date of final now. Decide on format, that is, all multiple-choice or not, and announce to all involved.
In the first hour, I did everything except page 6 on independence of path. In the second hour, I did page 6 in response to a question, but didn't do the "by hand" calculation on page 5.
In the first hour, I did everything except the last example on page 6. In the second hour, I did everything with 3 minutes to spare. One minor thing: on page 2, the example is not quite the same as in Lecture 18: they differ by a factor of 2.
Exam 2 to printer.
As written, this lecture is a little short. In the first hour, even after padding out the dicussion of why averages over shorter and shorter paths converged to the value of the function at the fixed endpoint, I actually ended class 5 minutes early. In the second hour, I did take the whole period, but I was definitely moving more slowly than usual. Also, this is among the most theoretical lectures of the whole semester.
(*) Unsure whether to drop Math 241? Try taking the practice test for the next midterm under timed conditions to see how you’re doing.
Got through notes as written.
I got through everything both times, though I had to rush the "Note" on page 6, which describes how, when the density is constant, that the center of mass is just the averages of coordinates over the region.
This lecture is fine, I had a few minutes to spare in both sections, and that's with an extended answer to a question that came up in both sections, namely is why phi only goes from 0 to pi.
This lecture is also fine, namely a few minutes short. I was feeling a little under the weather, so I skipped the straightforward calculation of the integral on page 3.
This lecture is also fine, especially as it's not necessary to discuss the linear approximation bit at the end in any detail. In fact, I skipped it in the second hour, in favor of a brief discussion of how the average of x - y over the triangle R is thus 1/3 and why that makes geometric sense.
Note: The 7th and last page of the notes is for reference only.
In both sections, I was unable to get through the general form of change of coordinates for triple integrals, even skipping the detailed evaluation of the integrals in the extended examples.
While personally I find the discussion of linear approximation for functions from R^{2} to R^{2} very satisfying, my guess is that it goes over their heads given how little exposure they have had with linear transformations.
Exam 3 draft due (Nathan and Kim)
This lecture is fine, even with the 5 minutes at the beginning for the general 3D change of coordinate formula.
For the "last time" part, Instead of the example of the torus in the notes, put up the unit sphere, including the formulas for r_theta and r_phi. By condensing some of the calculations, I was able to get through these notes in 40 minutes, leaving 10 minutes to discuss the visualization.
This lecture was fine, maybe even a little short.
Exam 3 to printer.
This lecture is too long as written, even assuming all the "previously" bits are up before the starting bell rings. In one lecture, I skipped page 6 and in the other the "Case 2" of non-simple curves the proof of Green's Theorem. Certainly the latter should be skipped, but even then page 6 will be rushed.
Curl and Divergence (§16.5).Notes
This lecture was an OK length given that I condensed the bit on page 4 labeled "Consider skipping" and didn't do most of page 6. Overall, I feel like the basic structure of the lecture is fine, but some of the details could be explained better. Possibly one should use more the language of derivatives as opposed to that of linear approximation.
2D flux and divergence: vector form of Greens Theorem (§16.5). Notes
Even going quickly, I could only devote 10 minutes to the heat equation stuff at the end, which isn't enough time to get through it all. If you slow down a bit, the first four pages of the notes can fill basically the whole 50 minutes.
Stokes theorem part 1 (§16.8). Notes
Draft of part 1 of final, covering roughly midterms 1 and 2 due. (Mostly Sue and James?)
Stokes theorem part 2 (§16.8).Notes
Draft of part 2 of final, covering roughly midterm 3 and after. (Mostly Nathan and Kim?)
This lecture is a good length.
Divergence Theorem (§16.9). Notes
This worksheet was new, and in most sections they only got through the (very long) first problem. Which is a worthwhile problem, but there's some other great stuff in there as well, so might want to revise. Or put some of it into the HW?
Final exam to printers
This lecture was a fine length.
Gauss’s Law (§16.9).Notes
This lecture is intensionally short so that there is time to do the ICES survey. It took me 40 minutes when I skipped the second half of the last page.
Conservative vectors fields in R^{3}, differential forms, and the general Stokes theorem.Notes
Skipping the second half of page 2 and simplifying Ampere's law to the case when the current is 0 made the notes as written take 35 minutes, leaving 15 minutes for a stirring summary the integral theorems and a hint at the general form of Stokes' Theorem.
Practical review for final