This summer has undeniably been about the busiest summer of my life. School’s starting up in 3 weeks, and so far I’ve gone through both Physics and Advanced Functions. After finishing that, I made the grand decision to work through calculus with the time I have left. Because why not? it just seemed like the sensible thing to do after finishing the “precalculus” of the Canadian curriculum.
Now, any normal person would’ve just went on JensenMath for free math lessons, but I didn’t really want to do any of that. I’ve used JensenMath in the past for Grade 11 Functions, and it’s incredibly helpful, but I just wanted lessons that were a bit more in-depth. This is when I decided to learn calculus off of Professor Leonard on YouTube instead, who posts his US college math lectures. His lectures are often over an hour long, but are extremely insightful when it comes to the actual mathematical concepts, which is why I’d recommend him so much.
So I started his Calculus 1 series. Originally, I was fully aware that Calculus 1 was much harder than the Canadian MCV4U, and I was willing to accept the challenge, since this was all done under my own discretion. I’ve looked into the concepts of calculus before, and they’ve all seemed pretty interesting, which is why I wanted more in-depth lessons in the first place.
Currently, I’ve made it to Lecture 3.4, which covers the second derivative test of functions, equivalent to the curve sketching unit in MCV4U. Most of the material I’ve learned so far hasn’t been horribly difficult, with two notable exceptions: trigonometric limits and related rates. Thankfully, neither of those topics are taught in the Calculus and Vectors course, but it’s notable they’ll likely serve as a roadblock if I ever take a math course in university. Related rate problems are especially difficult, not because the calculus is difficult, but because it’s often very difficult to interpret what a word problem wants you to do. I’ve always had trouble with word problems when it comes to math, and this is no exception. Take this example from the textbook I’m using:
Now I might look pretty stupid to anyone reading this who happens to know a lot about calculus, but I had just about zero clue how to even start this problem when I first laid my eyes on it. The actual calculus isn’t difficult at all; just get an equation that ties in all variables involved, and take the implicit derivative with respect to time. But the method to get to that setup is something I could never work out. You have to figure out on your own to use similar triangles between the man and the streetlight in order to solve it, something that isn’t immediately obvious after inspecting the problem.
Calculus has a lot of other concepts not taught in MCV4U as well, one of them namely being integration. I’m hoping I won’t find that section awfully difficult, since Calculus 1 introduces a mere introduction to integration methods, rather than going in guns blazing. Also, Calculus 1 doesn’t actually have anything relating to vectors, so I’ll just have to wing that when I actually get to it in school. But for everything else, I’ll be pretty much ready for. That’s why self-studying will hopefully be all worth it in the end.