I had another pitiful, write-off type of week on KA. I watched eight videos and attempted one exercise on Green’s Theorem but didn’t pass the exercise. I’ll go into more detail below, but I still don’t have a great understanding of what the hell is happening with G.T. which is super disappointing considering I’ve been working on it for going on 13 years now. 🙄 I think I probably have a better understanding of what’s going on in the questions now than I was the first time working through them – I have a better grasp on the notation than I did before – but, as I’ll talk about below, I still don’t understand why the questions work the way they do or even how to solve them…

Part of the reason why my progress this past week was so abysmal was because I had a procedure done that more-or-less KO’d me for ~two days. The procedure was to try to figure out why I’ve been feeling so sick for the past six months but unfortunately I didn’t learn anything new from it that could potentially help me recover. The good news is that I can cross some reasons off the list of things it could have been which is a relief. But, apart from that, I’m not any closer to figuring out what’s wrong with me and/or figuring out how to fix it. 😒 I’m thinking more and more that I just have some stupid version of long covid which has taken hold of my stomach. I can’t say for sure, but I think it might be getting better but it’s very hard to tell. I have a follow up doctor’s appointment today so hopefully we’ll be able to come up with some new plan of attack for me to get on top of it.

Anyways, below are three questions from the exercise I worked on. I got two of them wrong, and my notes are wrong but I figured I’d add them here to show how I thought I was supposed to solve them:

Question 1

Question 2

Question 3

The question just above is the type of question that I really don’t understand. As far as I can tell, I’m supposed to go from the double integral to a single integral by integrating the two terms in the double integral’s integrand, one with respect to x and one with respect to y. The part I don’t understand is how I’m supposed to know which term goes with which variable. KA’s answer makes it sound like, “because cos(y) would be easier to integrate with respect to y, you integrate it with respect to y.” If that is indeed what it’s saying, that seems like stupid reasoning and doesn’t make any sense to me. 😡 That’s why I think I must be missing something here, but I can’t figure out what it is. In any case, I’m going to reattempt this exercise early this coming week and will try to solve these questions simply by looking at the integrand and figuring out which terms/expressions would be easier to integrate to each variable and then try to solve the questions from there. 🤷🏻‍♂️

And that’s going to do it for this post… Once again, not a very lengthy post but I still don’t have the energy/motivation/desire to work on KA these days. I’m hopeful that eventually my health will go back to normal (and I’ll have a WAY bigger appreciation for what ‘normal’ means if and when that day ever comes), but until then, I’m honestly just happy that I was able to get a bit of work done and write this short post for no other reason than to keep the streak of working on KA and posting about it alive.