It was another poor effort for me this week on KA. 😑 I only made through four videos… I got a better feel for how to solve exact differential equations (i.e. I think I understand the formula/pattern a bit better now), but I made little progress understanding what’s going on, let alone why this type of math works the way it does and the bigger picture of differential equations, in general. So, ya… I’m pretty disappointed with my overall effort. For some reason, I’m reluctant these days to push myself on KA. I think it’s mainly because I don’t understand what’s going on and therefore am struggling to grind through it. There might be other reasons, but regardless, I need to come up with a strategy to push myself harder each week. That said, I did make some progress this week, so I’ve at least got that going for me which is nice. I’m also finally ready to talk about the project I’ve mentioned a few times in previous posts, which I’ll get into at the bottom of this post. 👇🏼
Video 1 – Exact Equations Intuition 2 (Proofy)
As you might be able to tell from the title, this video was a continuation from the video before it (the one I talked about at the end of my last post). When I watched the video and got to the end where Sal summarized how exact equations work, I understood ¼ of what he was talking about. At the end of the week, I think I understand closer to ¾ of what he was talking about, mainly the how of how exact equations work. I should mention that the square brackets in my notes above was me writing in the notation/equations Sal was referring to when he was talking, not something he literally said out loud in his summarization.
I just spent a few minutes trying to reiterate what Sal said and put it into my own words, but I failed miserably. Determining whether a differential equation is exact is fairly involved with a number of steps, then you have to figure out what Xi is (pronounced ‘Zzzi’ and denoted with that pitchfork looking thing) which ends up somehow simplifying the OG equation… 🤔 I don’t understand it, but I know you have to go back and forth between the OG equation and the antiderivatives and partial derivatives of all the expressions denoted with M and N…
The next three vids were all examples Sal worked through which will hopefully make the how of how to solve them a bit more clear.
Video 2 – Exact Equations Example 1
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I think my notes actually do a pretty decent job here of showing how to solve an exact equation, so I’ll let them speak for themselves. One thing I’ll also say is that the final solution to this problem is (ycos(x) + 2exey) + (sin(x) + x2ey – 1) = 0, but I don’t know what it means for that equation to be the ‘solution’… 😔
Video 3 – Exact Equations Example 2
This video and the next were questions that were set up the same way as the one in the previous video. Sal started with an equation and worked through it to 1) determine that the equations were in fact exact, and 2) solving them to find Xi. You can see from my notes that I sort of got a feel for how to solve them, but I can’t put into words what I did. It’s disappointing that I don’t know what’s going on, but nonetheless, I think I’m making some progress, in general, and will (hopefully) eventually figure it out. 🥵
This is the last video I made it through:
Video 4 – Exact Equations Example 3
And that was it for this week… I’m not going to say anything now about how I need to work harder this coming week (although I do…) since that’s what I’ve said the past few weeks and it hasn’t amounted to anything. I have nine videos left to get through in this unit which I should be able to do in two weeks at the most. Finger crossed that I get it done. 🤞🏼
On a different note, the project I’ve referred to in a few of my last posts is a program I’ve been working on for the past year called CodaKaizen. It’s a program that helps people with self-development and, in a way, relates to everything I’ve done here on Solve For Why and relates to my self-improvement journey, in general. The program gets people to two things; set weekly goals for themselves across a number of different categories, and write a story about a formative experience they went through using the Hero’s Journey framework. I wrote a Hero’s Journey story about myself which you can find here. You can also check out the website I’ve created for the program here. I’m hoping to turn the program into a business, which I think could be a long shot, but given how dedicated I’ve been to my own self-improvement over the past few years and everything I’ve learned (all of which has gone into the program), I think I have a chance of making it work. I would LOVE to spend the rest of my life helping people turn into better versions of themselves, so I’m really hoping the program will be successful.
Almost six years ago I literally told myself, “if I can teach myself calculus, I can do anything”. That goal has since morphed into, ‘if I can finish the math section on KA, I can do anything’. That’s why over the last few posts I’ve mentioned that I NEED to finish KA, so that I truly believe I can turn CodaKaizen into a business. So fingers double crossed I can have a good upcoming week and make some quicker progress on KA. 🤞🏼🤞🏼