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.
In both sections, got through the plane example but not the triple product or anything after that.
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.
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.
Exam 1 due.
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.
Exam 1 to printer.
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.
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.
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 (Patrick 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 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.
Got through notes as written.
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.
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 Patrick)
This lecture is fine, even with the 5 minutes at the beginning for the general 3D change of coordinate formula.
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.
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.
Draft of part 2 of final, covering roughly midterm 3 and after. (Mostly Nathan and TBA?)
This lecture is a good length.
This worksheet was split in half from the corresponding one in 2016.
Final exam to printers
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.
This is the second half of the Stokes' theorem worksheet from 2016.
Final exam to printers
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.