I got my ass kicked this week KA-wise and health-wise. 😒 I got through a whopping FIVE questions on the course challenge, getting 4/5 correct which is the only thing I can be ‘proud’ of this week. I also didn’t watch any videos from the Steve Brunton playlist I talked about in my last two posts. So ya… overall, it was a pathetic week. My health took a pretty big negative turn which I assumed would happen since it’s been a up and down over last seven months, but mentally and emotionally it was more difficult this time since it seemed like things were going in a better direction the last few weeks. It’s really hard to tell on a daily or even weekly basis if things, overall, are improving or regressing though, so I’m still hopeful that although it was a really crappy week, it’s possible that it’s getting better all-in-all. 🤞🏼 In any case, for the millionth time in a row, it’s going to be a very short post this week. I’m praying to all the gods (math and regular) that one day I’ll be back to normal and can get back to studying a decent amount each week and writing half decent posts. 🙏🏼

Here are three of the five questions I worked through this week:

Question 1

As you might be able to tell from the last screen shot, I cheated on this question. I tried a couple of different methods to get a solution close to the four that were given but couldn’t figure it out so I Googled how to find the speed of a vector-valued function. Once I was shown the formula, it wasn’t too difficult just to input the functions into the equation and do the algebra to solve.

Question 2

This is the question I got wrong this week. (I rewrote my notes in the photo above to show how it should be solved, although I don’t think I did the proper way.) I would have gotten it wrong anyways, but the stupid mistake I made was that I found the partial derivative of each component of f as opposed to finding the partial integrals. 🤦🏻‍♂️ (Also, is “partial integral” the correct way to say it? I’m not sure.) If I had found the partial integrals, I may have gotten the question correct as I quickly remembered how to solve these types of questions once I looked at KA’s answer, but in all likelihood I think I would have gotten it wrong, even still. I don’t really understand why F is a single equation whereas f is a vector equation. I think it’s because F is a scaler-valued function whereas f is a vector-valued function, but I don’t know. It’s incredibly disappointing that I’m this far into MC and I don’t know what’s going on with the notation… 😢

Question 3

This question was pretty straightforward as all I had to do was integrate the expression with respect to y, z, and then x which wasn’t too difficult at all. In fact, I actually found doing this type of question ‘fun’ (as far as doing math can be ‘fun’, anyways) and it was super satisfying and relieving to get it correct. It was the last question I worked through, and so I was happy knowing that even though I got my ass kicked this week, at least I’ve learned some stuff over the past ~6 months when it comes to multivariable calculus.

Like I said, I’m praying to all the gods that will listen that my health goes in a better direction this coming week and that I can make some decent progress on KA. I would LOVE to at least get through the course challenge. I have 17 more questions left to get through so in theory it should be doable. Even if I get a bunch of questions wrong, I don’t really care since it will just be a good excuse to go back and review what I got wrong and hopefully make more sense of it going through it a second time. That’s usually what ends up happening so getting a bunch of questions wrong would be fine with me. Plus, even if I do terrible on the test, it will still be progress moving forward. After so many crappy weeks, I’d rather make slow progress than no progress at all!