Although I got my butt kicked this week on KA trying to get through the Multivariable Calculus Course, I’m happy with my overall effort this week and what I was able to learn. I only got through seven questions on the C.C. but watched five videos from the Engineering Math: Vector Calculus and Partial Derivative Equations playlist made by the YouTube creator Steve Brunton. These videos helped me have a handful of concepts sink in a bit more, but there’s still plenty of things that I still find confusing. Although each video was ~20–25 minutes in length, and even if I include the questions I worked through on the Course Challenge, I’m pretty sure I didn’t spend five hours studying math this week. 😒 What’s way more important to me, however, is that I think I **knock on wood** may FINALLY be starting to turn a corner in terms of my health. I REALLY don’t want to jinx it but I felt better this week than I have since early November, and it seems like things may finally be going in the right direction. I’m ready and assuming that my health will swing back the wrong way (it’s been up and down for the last seven months), but I’m starting to believe it’s possible that one day I will eventually feel better. So considering that, plus the fact that I did learn some things on KA this week, it was one of the best weeks I’ve had in a LONG time. 😮‍💨

Here are the five videos I watched this week on from the Steve Brunton playlist:

Like I said, I got my butt kicked working through the C.C. this week and only got three out of seven questions correct. I surprisingly took screen shots of every single question, so here they are:

Question 1

I ended up getting this question correct but Googled it before submitting my answer and didn’t really know what was going on. I understand everything in this question except for the Jacobian, which I’m pretty sure is the main part of the question… I’ll most likely have to go back and redo some of the exercises after finishing this first attempt at the C.C. and, assuming that’s the case, am hoping to make more sense of the Jacobian when I go back to review those exercises/videos.

Question 2

I don’t think I would have gotten this question correct if I hadn’t gone through the Steve Brunton videos over the past few weeks. I don’t have any trouble finding the determinant of a 3×3 matrix but I used to always get the vector operations (gradient, divergence and curl) mixed up in my head and could never remember which operation used the determinant, partial derivatives of P and Q, etc. It was pretty satisfying and relieving getting this question correct and feeling confident that I had a decent grasp of what I was doing as I worked through it.

Question 3

I cheated on this question and still got it wrong. I looked up what the Laplacian was because I couldn’t remember and then still wasn’t exactly sure if I was solving the question correctly as I worked through it. As far as I can tell, I WAS doing it correctly but then I ended up getting the algebra wrong. It probably serves me right for cheating on the question… 

Question 4

There’s not much to say here other than that I now find these types of questions fairly easy which is a big relief. It’s also something that in retrospect I’m pretty proud of considering that a year ago I would have had no clue what this question was talking about.

Question 5

I did the partial derivative on this question wrong but even if I had done it correctly, I wouldn’t have remembered the Trig Identity that 2sin(x)cos(x) = sin(2x) so I was doomed to fail from the start… You can see in my second note that I did work through the partial derivative afterwards which wasn’t too hard, so I’m annoyed that I didn’t get that correct in the first place.

Question 6

I knew what this question was asking me but couldn’t remember that I had to find the partial derivatives of x and y of the vector field to solve it. Once I saw KA’s answer, doing the math to get to the solution was pretty easy.

Question 7

Again, this was another Jacobian type of question where I got my butt kicked. I straight up don’t remember anything about the Jacobian, but I think it has something to do with scaling functions when reparametrizing them to integrate them. That could be completely wrong though…

Although I’m somewhat disappointed with how this week went, it could have been worse and for the first time in a LONG time I’m feeling optimistic that it’s possible that soon I’ll be feeling more like myself and can get back to putting in some decent effort into KA on a weekly basis. I’m SO close to finishing off the Math section in KA and am starting to get pretty fired up about getting to the end of it. Part of why I’m getting more pumped to get through it is because the Steve Brunton videos I’ve been watching have talked a lot about physics which is the next subject I plan on studying on KA. I think it’s unlikely I’ll be done the Math section before Week 261 (a.k.a. the start of year six… 😳) but that’s what I’m going to aim at. Hopefully I’ll have a more successful upcoming week so I make some decent progress towards achieving that timeline. 🤞🏼