I once again didn’t have a great week on KA. I’m still getting rocked by vector calculus and still don’t really know what’s going on… I know I’ve said this a million times before, but I do feel like I’m getting closer to figuring it all out. The problem is I don’t know how much further I have to go, so even though I feel like I made a bit of progress this week, I don’t know if I got 5% of the way closer to the finish line or 0.5% of the way there. In my post last week, I added a video from Professor Leonard and said I wanted to watch the whole thing. It’s a ~3.5 hour lecture and I only made it through 2 hours, BUT it did help me wrap my head around some of the notation used in this unit which I think is pretty important in the big picture. Watching that video was also helpful to hear and see the concepts being presented in a different format and from a perspective. So, overall, it wasn’t the best week but it could have been worse. 🤷🏻‍♂️

There were a handful of insights I gained while watching the Professor Leonard video (which is below), and one of the key notational insights I understood was what dS represents. (To be clear, I’m not 100% certain I have it figured out properly, but I think I’m a lot closer to fully understanding it’s meaning, at the very least.) The S in dS represents a 2D vector and stands for surface. To be fair, I already knew that the S stood for the word surface, but didn’t realize that I should think of dS as a section of 2D area on a 3D surface. (More specifically, I should be visualizing it as a tiny, tiny 2D section of area on a 3D surface.) I don’t think knowing this is going to be a HUGE game changer for me in my understanding everything that’s going on, but having a better grasp on what the notation is communicating always makes things easier to interpret so I’m hoping the rest of unit will go smoother knowing this. But in any case, this is the video I’m talking about:

This week I only made it through three videos, all from the section 3D Divergence Theorem. They were somewhat easy to follow along with, although I wasn’t able to grasp the bigger picture of what’s going on with the 3D divergence theorem. I also attempted the exercise from that section (about a million times) but wasn’t able to get through all four questions without getting one wrong so I didn’t end up passing it. The annoying part was that there were two types of questions, one that was more about doing the actual math involved with the 3D divergence theorem and the other type being more of a word problem, and the math questions I was able to answer correctly relatively easily but I kept getting word questions wrong… 😠 So, here are seven of the math questions and my notes from each, and then at the end is an example of one of the word questions:

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Once I figured out the pattern for solving the math questions, they were super easy. They gave me a lot of good practice doing partial derivatives and integrals which I found helpful. I had to use the reverse chain rule a couple of times and also reviewed finding the integral of tan(x) which both were good refreshers. I didn’t spend enough time thinking through the word questions and would more-or-less just take a guess at them after reading through them quickly one time. I don’t think it will be too hard for me to actually understand what conditions are necessary for the 3D divergence theorem to apply, so I think I should be able to get a handle on those questions early this coming week. I’m optimistic I’ll be able to get through the exercise on Tuesday. 👍🏻

I have two weeks until my 34^th birthday. 🥳 There are 15 videos, three exercises, and this final exercise for me left to get through to finish off the content in Green’s, Stokes’, and the Divergence Theorems (400/600 M.P.). I think it’s possible for me to get through it all int he next two weeks, but it will be tough and will be a sprint to get through it all. It’d be pretty sick to have all the content in Multivariable Calculus finished off before my birthday, so I’m definitely motivated to get it all done and think I have a decent shot at it. That way I could start my 34^th birthday working on the unit test and then course challenge of M.C. and be SO close to being done calculus. It’s definitely taking a lot longer than I thought it would (about 3 years longer 🙄) but the finish line is getting closer. PLEASE math gods, let me have a good week so I can finally get to the end! 🙏🏼 🙏🏼 🙏🏼