I’m incredibly relieved to say that this was the best week I’ve had on KA in literally months. I FINALLY finished the Green’s, Stokes’, and the Divergence Theorems unit test and, even more surprisingly, actually think I’ve gotten over the hump of understanding the gradient, curl, and divergence operations in vector calculus. The tipping point came after watching a handful of videos from a creator on YT called Steve Brunton which I’ve added just below. (I’m not 100% sure but I believe he’s a math professor at the University of Washington, but I could be wrong about that.) Finally, after ~20 weeks of trying to figure out what’s going on with vector calculus, the notation and operations, and how I visualize it all coming together seemed to click for me this week. I’m definitely not all the way there and still don’t completely understand Green’s or Stokes’ theorem, but they both seem much simpler now that I have a better grasp with what’s going on with the vector operations. So, suffice it to say, after 65 weeks of working on Multivariable Calculus (I went back to check and realized I started MC in Week 185… 😳) I’m VERY happy and relived right now that I will finally be starting the course challenge next week. 😮‍💨

I’m annoyed with myself that this is becoming a habit, but I once again don’t have much time to write this post this week. So, without going into detail, here are the five videos from the Engineering Math: Vector Calculus and Partial Derivative Equations playlist I started from Steve Brunton:

This was the first video I watched but it is actually the eighth video in the playlist. I Googled Green’s Theorem vs Stokes’ Theorem one morning and it was one of the first results. I thought the video was really well produced and afterwards realized it was part of the playlist I mentioned so I decided to watch the entire playlist from the beginning. These next four videos are the first four videos from the playlist:

As I mentioned, I think these videos are really well produced. I like the way he writes out his notes in front of him. Although I’m excited and planning to start the course challenge next week, I’m also planning to continue watching this entire series of videos and am hoping to make it through all of them. There are 23 videos in total, most off them around 20 minutes in length but some of them are more than 40 minutes, so it will take me a bit of time to get through them all.

I had a slow start to this week and it took me until Friday to get through the final exercise from Stokes’ Theorem. By the end of the exercise, I finally had a decent grasp on how to answer the questions, but I still didn’t (and still don’t) really know why the theorem works… Anyways, here are two example questions from that exercise:

Question 1

Question 2

Like I said, even though I’m getting better at solving these questions, I still don’t really know what’s going on with them, but I’m starting to better understand the concept of a vector field, F, going through a surface or a volume and the difference in the notation between the two. Honestly, I’m not even sure if any of that was correct or made sense, but I still feel like I’m making progress!

When I started the unit test on Friday, I definitely didn’t think I was going to get through it by the end of the week. Having watched a handful of the videos I included above by that point, I was starting to feel better about using the different vector operations and had a better understanding of which operations were to be used with which theorem. It took me Friday and Saturday but I managed to get all ten questions correct on my first try! Here are five of the questions I worked through from the test:

Question 3

Question 4

Question 5

Question 6

Question 7

As I said, I don’t have time to go through the questions above, plus I think my notes are somewhat legible and hopefully easy to understand, so I’m going to leave it there for this post.

Looking ahead, after the course challenge for MC I have two more subjects left to get through, Differential Equations and Linear Algebra. The way both of them are set up is different than any of the other subjects that I’ve worked through in KA so far as neither of them have any MP for either subject. 🤔 They each have three units which are mostly made up of videos and articles and four of the six units have no exercises to do. I feel like and entitled brat by saying this, but I’m a bit disappointed that there are no exercises in these subjects as that’s what usually helps me most understand what’s going. That said, although it may be harder to understand and make notes on for my posts, I think it will mean that I’ll get through both subjects a bit quicker than usual.

I’m finally starting to see the light at the end of the KA Math tunnel which is pretty nuts. I don’t want to get too far ahead of myself, however, as I’m pretty sure this course challenge is going to be insanely difficult. 😐 As always, fingers crossed! 🤞🏼