Green is for "todo" items
Absences
Nathan: October 12-15
Jake:
Burak:
Xuan:
Nathan's notes for what was actually covered in lecture. I write the "Last time" parts up on the board before class starts and usually talk about them for 1 or 2 minutes (or even less). Also "This lecture is fine" means I covered everything with a minute or two left over.
This lecture should take 40 minutes, leaving 10
minutes to discuss the syllabus, assuming you start on time. When
covering distance in n-dimensions, it would be better to first
compute the distance from the origin O to P and also to label the
points as O and P in the 2D and 3D examples.
2025 and 2026: I got through the lecture in about 35 minutes.
Final exam schedule request due.
Do not cover the derivation of the dot product
on page 6. You want at least 15 minutes for the dot product,
which requires skipping position vectors and some properties of
the vector operations. Also, while we usually think of theta as
the smaller of the two angles on page 5, the formula also works
for the other one as the cosines are the same.
2025 and 2026: I had 20 minutes left for the dot product in both
sections. In one case, I ended five minutes early.
This lecture is way too long as written. You should
skip the discussion of regression and complete the discussion of
projection and work in about 15 minutes. I usually start the
plane examples/problems (bottom of page 4), with 20 minutes left.
This is OK, but the answer A2 was packed into just a couple
minutes.
In 2026, I ran out of time for A2 in the second hour.
Only cover through the triple product on page 5. Expect to have
about 5 minutes each for the example at the bottom of page 4 and
the triple product.
2025 and 2026: In one section, had only three minutes for the triple product.
I find there's not time for both the plane example on page 6 and the Hopf fibration video. I do the video, and hit the 3-variable function at the top of page 7 with 10 minutes left.
Assign midterm exam rooms based on current enrollments (Nathan)
Using the Interactive Gallery to breeze through quadrics, I start in on limits at 20 minutes in. I then cover everything except the example on the middle of page 6.
Cover up to the top of page 5, just before "rules for limits".
This leaves time enough to do the limit pictures Mathematica
notebook and tell the sad story of the Sleipner A.
2025: In the first hour, I hit the second example only 30 minutes
in and ended 5 minutes early. For the second hour, I had only 5
minutes for the story of the Sleipner A.
Exam 1 draft due
I get through page 6, but have to make
conscious effort to keep the pace up. Typically start partial
derivatives with 10-13 minutes left.
2025: I slightly
shortened the limit laws discussion by only writing the quotient
rule and started partial derivatives at the expected time.
I cover everything except the proof of the first theorem at the bottom of page 5, but it's a little tight.
Exam 1 to printer.
I drop the explicit error term on Page 3 and sometimes don't get through the "Alternate viewpoint" section. 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 theoretically, which 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.
I cover everything in the notes and the lecture is a nice length.
After the due date of a homework assignment, click the "VIEW ANSWER KEY" button at the top to see a complete worked solution to every problem.
This lecture is a nice length and I was able to get through it all without working too hard.
This was fine when I skipped any detailed discussion of why x^3 is unstable. I finished page 4 at 30 minutes in with 10 minutes left for each of pages 5 and 6.
I skip the asides on page 5 and have about 10 minutes for the example on page 6.
This lecture is a good length. There is time at the end to discuss why the local max in the last example is the absolute max, as outlined on page 6. I don't usually cover the bottom part of page 6.
This is fine, I usually finish the examples and cycloid discussion at 25 minutes in.
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 is fine. I needed about 15-16 minutes to do everything after "Understanding these integrals"; once I did it in 13 minutes which was kinda tight.
Should learn date of final now.
Draft of Exam 2.
This lecture is a good length. I start page 4 with about 20 minutes left and need 8 minutes to cover the last example comfortably.
In the first hour, I did everything and in the example on page 5 added a discussion of why we should expect the answer to be positive geometrically based on the first half of the lecture. In the second hour, I had to drop the "by hand" part of the calculation on page 5. In both hours, I started the discussion of the Fund Thm of Line Integrals with 20 minutes left.
Sometimes I've managed to do everything except the last example on
page 6 (F = 1/(x^2 + y^2) (-y, x)), but other times I've strugged
just to get through stating Theorems A and B (which one definitely
needs to do).
2025: I had the second experience both times, but the mic was out.
Exam 2 to printer.
As written, this lecture is a little short. I pad it out with a discussion of why averages over shorter and shorter paths converged to the value of the function at the fixed endpoint, but even then I sometimes end a little early. This is among the most theoretical lectures of the whole semester.
This is fine.
(*) Unsure whether to drop Math 241? Try taking one of the practice tests for the next midterm under timed conditions to see how you’re doing.
Solutions to all discussion worksheets are posted on Canvas under Files.
I get through these notes as written. In 2019, got to polar coordinates with 20 minutes left.
I cover everything, though I need 25 minutes to do the "Applications of Integration" properly and usually only have 20, resulting in some rushing at the very end.
This lecture is fine, even with an extended answer to the question that always comes up, namely is why phi only goes from 0 to pi. I need at least 15 minutes to do "Alternate coordinates" section (bottom of page 4 to end).
I skip the straightforward calculation of the integral on page 3, and usually finish the cylindrical example at 27-30 minutes in. If time remains at the end, I give a brief discussion of what slices look like in spherical coordinates.
I skip talking about linear approximation (bottom of page 5 to end) and instead give a brief discussion of how the average of x - y over the triangle R is thus 1/3 and why that makes geometric sense.
I always skip the indiciated pages 4 and 7, though I will state the aside on page 7 if there is time. While personally I find the discussion of linear approximation for functions from R2 to R2 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
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 40-44 minutes, with the remaining time used to discuss the visualization; the latter is better with 10 minutes.
This lecture was fine, maybe even a little short.
Exam 3 to printer.
2016: This lecture is too long as written, even assuming all the "previously" bits are up before the starting bell rings. I skip worrying about non-simple curves in the "proof" of Green's Theorem (Case 2), and only do the bit of page 6 where I derived the formula for the normal vector from the velocity vector.
I usually cover the the first five pages, though typically with only 5 minutes for the part after the separator. Sometimes, I only get to the separator, and I never do page 6.
HW due Dec 2 instead of Nov 30 so everyone gets to do the next worksheet before it is due.
I just cover the first four pages, skipping the application about heat flow entirely. If one has a five minutes at the end, one could redo the solid cone example with another vector field, e.g. (x, 0, 0) or the easier (0, 0, z) so that the divergence theorem tells us we are computing the volume.
This lecture is much longer than it looks. I made one change: moved computing the curl of the vector field in the example, namely F = (-y, x, yz), forward to page 2 since it's more generic than than F = (y, 0, 0), which I also did. Only putting the top half of the first page on the board to start, I hit the top of page 4 with only 10 minutes left both times, which is tight even skipping the bit at the end about the lower hemisphere.
This lecture is a good length.
2016 and 2018: This lecture was a fine length. 2019: In the first hour, I almost ran out of material; in the second hour, I didn't quite get through it all. Both results were fine.
This lecture is intensionally short to allow time for them to fill out the (son of) ICES survey. I completely skip the calculation of div E on page 2, and then it takes 42-43 minutes with some discussion of the second half of the last page.
Instructors should do Son of ICES today.
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.