I would grade my overall effort this week as a C+ as it definitively could and should have been better. I have the same usual excuses as the past few weeks… First of all, I still feel like crap. I’ve also been allocating a lot of my time, energy and focus into this other project I’ve been working which, again, lead to me not spending enough time on KA. (As a side not, I’m making a LOT of progress on this new project I’m working on – call it CK – which, considering I’m getting my ass kicked by S.T. and this virus, is about the only thing that’s lifting my spirits these days.) Finally, I’m still not really understanding either the how or the why of Stokes’ Theorem which makes it hard to stay motivated. A silver lining from this week is that I finished off the exercise from the Stokes’ Theorem section which I was happy about, but only because I 1) had seen a lot of questions before having failed it so many times, so I knew the solution before submitting my answer, and 2) even on the questions I hadn’t seen before, I had memorized the pattern of how to solve the questions but still essentially had no clue what was going on in them. It seems like I every week I’m getting closer to figuring it all out, but I’ve also been saying that for ~10 years so it seems like that could be BS. In any case, this is the longest opening paragraph of all time so I’m going to stop rambling and get on with his post. 🙃
Like last week, I once again have very little time to write those post so I’m going to rush through it once again. As I mentioned, I finished off the final exercise from Stokes’ Theorem on Wednesday this week. It wasn’t too difficult and it helped me a bit to understand how to answer these types of questions but still didn’t make it clear why Stokes’ Theorem works. Nonetheless, here are two questions from the exercise and my notes from each question:
Question 1
The only reason why I got this question correct was because I had the pattern of how to solve it memorized. I essentially have no idea what’s going on with the function P and don’t really understand how it relates to the single line integral or the double surface integral. One silver lining is that I have a fuzzy idea of the difference between the two types of integrals, but I definitely don’t understand the bigger picture of what’s happening, in general, or what’s going on in the question, in particular. 👍🏻
Question 2
Even though I don’t really know what’s going on with these questions, the math feels very satisfying to work through. I’ve memorized how to use the vector curl operator which certainly helps and is enjoyable to use now that I can use it without thinking. Plus, I weirdly like writing out all the different forms of notation. I like the calligraphy feeling of it and the look, so I’ve at least got that going for me, which is nice.
I also made it through the three articles in the following section Stokes’ Theorem (Articles) but they unfortunately didn’t help much to understand S.T. any more than I already did. Nonetheless, here’s literally screen shots of the entire third article which I’m only adding here to fill out this blog post. 🤷🏻♂️
To try and understand what the hell is happening, I once again branched out and tried watching a few other videos on Stokes’ Theorem. The first two videos below were really well produced and very informative. The third video below was also helpful but only in the sense that it confirmed my general, low-resolution grasp of what’s going on with Stokes’ Theorem.
Finally, just this morning I was looking up other videos to try to watch to make myself feel better about not putting in enough effort this week and came across the video below from the creator Professor Leonard. His lectures have helped me a fair amount in the past so I’m hopeful that this video will help me wrap my head around what’s going on with S.T. this coming week. Plus, it’s 3 hours long so watching the whole thing through will be an easy way to get close to reaching the 5 hours of studying this coming week that is always my bare minimum.
And that’s it for this week… I only have three videos and one exercise left in Green’s, Stokes’, and the Divergence Theorems (400/600 M.P.), but unfortunately still have 18 videos left to watch. 😑 My birthday is 20 days away and it’s possible that I could get through it all by then, but I feel like it’s unlikely. As always, it won’t be the end of the world if I don’t, but I do think it’s a good goal to aim for. However, as always, I’m not going to rush through it all for the sake of making progress at the expense of actually understanding what’s going on. Even still… I REALLY hope I can finish this off by then, or at least sooner rather than later! 🤬