I’m happy to say that I passed the Parametric Equations, Polar Coordinates, and Vector-Valued Functions unit test this week (on my first try!) and am now into the FINAL UNIT of calc.2, Series! It took my three days to get through the 15 questions on the unit test. I had to look up 1 or two formulas throughout the test but, for the most part, I managed to answer all the questions from memory without having to review my notes. That said, there were still a number of questions that I was only able to answer because I had the formulas memorized and didn’t really intuitively understand what was going on. Nonetheless, I’m still happy that I passed on my first try and, to give myself some credit, definitely have a MUCH better understanding of parametric equations, polar coords, etc. than I did a month and a half ago. 💪🏼😤

As I mentioned, it took me three days to get through the unit test and finished it on Thursday. I got through some of the questions in just a few minutes but others took me ~20-30 minutes to workout. I also used Desmos on a bunch of questions to make sure I was on the right track. Here are three questions I worked through on the test:

Question 1

I still find the notation, dy²/dx², a bit confusing. I think what it’s saying is you have to find the double-derivative of y(t), a.k.a. you find y’’(t), and find the the first derivative of x(t) and then square it, a.k.a. (x’(t))². I might be wrong about that though. 🤔

Question 2

As you can see, the algebra I used to work through this question wasn’t the same as what they did in the KA answer. I’m not sure if this is technically correct, but I find it easier to think of x and y and x(t) and y(t). I think my algebra might be wrong where I simply input 2 and 9 in place of x(t) and y(t) respectively. I think my way of doing it is correct, generally speaking, but not proper in a technical sense.

Question 3

Once I got through the unit test I was pumped to finally start the following unit, Series, on Friday. I was a bit shocked when I counted the number of videos and exercises and realized that altogether there are 60 videos in this unit (😳) and 20 exercises. I managed to get through the first 6 videos by the end of the week which I was pleased about but only finished one exercise. The 6 videos I watched were all from the first section of the unit which was titled Convergent and Divergent Infinite Series. I’ve learned about convergent and divergent functions in the past but don’t remember too much about them. Here’s a page from my notes that goes through 4 functions of series that converge or diverge:

First off, my understanding is that if a function converges, that means it gets closer and closer to specific value whereas if a function diverges, it doesn’t. My understanding is also that if the variable with the highest degree in the numerator is the same as in the denominator, the function will converge and, if not, it will diverge. 

Lastly, a few of the 6 videos I watched went through the difference between an infinite series and a partial series, and gave their respective notation. Since I haven’t learned much about either types of series, I’m not going to go into any detail about what they do/how they work, but here are two pages from my notes that summarize most of what I watched:

The end of calculus is finally in sight! Even though I still have 54 videos left to watch and 19 exercises to get through, I’m still aiming to be done this unit, Series (80/2,000 M.P), by the end of the year. Thinking about it, I’m almost a bit sad that this goal I’ve been working towards for the past ~3.18 years is finally coming to a close. Once I finish calculus, I still will need to get through the course…….

Shit… I just looked at KA to see what my next course would be and realized there’s another calculus course! It’s called Multivariable Calculus and it has 5 units in it and is 4,800 M.P. in length. So I guess I’m not going to be finished all of calculus by the end of the year… Off the top of my head, my goal now is to still get through calc.2 by the end of the year but then get through the Multivariable Calculus course by the end of the school year.