 Welcome to our lecture series Math 12-10 Calculus 1 for students at Southern Utah University. Let me quickly introduce myself. My name is Dr. Andrew Misseldine and I will be your professor for this course. Calculus 1 without me overselling it is probably going to be one of your favorite mathematics courses you're ever going to take and why is that? Well, there's probably two types of students out there and you're one of them, I imagine. First, there's some people just love everything mathematical and scientific and analytical and so you just gobble this stuff up and Calculus is going to be more of that delicious logical candy for you. From other people, other students might be a little bit more skeptical like, when am I ever going to use math? We learn all these hard things, but when am I ever going to use it? Let me talk to that group of students just for a moment. I like to compare Calculus to the Karate Kid movies. That is the original ones from the 80s. I grew up watching these movies. I love them a ton, the kicking and the punching and things like that. So really quick synopsis for those who are unfamiliar with the movie. There's a teenage boy, Daniel LaRusso, who moves to a new town. He's having a hard time fitting in. There's a girl he likes, but it turns out there's another guy who likes the same girl. And who belongs to a karate dojo known as the Cobra Kai. And so in the rivalry, the Cobra Kai have a bad habit of kicking Daniel's butt all the time. And so after he gets the tar kicked out of him several times, a wise old Japanese man who befriends Daniel, his name is Mr. Miyagi. He takes him under his wing and he promises he'll teach him karate so that he doesn't have to get beat up all the time. Well, when Daniel starts going to Mr. Miyagi's house to learn karate, Mr. Miyagi is never there. He leaves notes and tells Daniel that he has all these chores to do. Like some of the things Daniel has to do is he has to wax all of Mr. Miyagi's cars, which he has a lot of classic cars. He has to paint Mr. Miyagi's fence. He has to sand Mr. Miyagi's deck and just to name a few of these chores he has to do. And this goes on and on and on for days and days and days. And so after a while, Daniel just gets extremely, extremely frustrated with Mr. Miyagi. He's like, why am I doing all these chores for you, right? I thought you were going to teach me karate. And so what then Mr. Miyagi does for Daniel is he changes the context. Daniel believed he was doing all these chores when, in reality, Mr. Miyagi was having him practice muscle memory, various karate moves like lifting up his arm and waxing the car, just to name a few examples. And so Mr. Miyagi shows that all these muscle motions that Daniel's been doing over and over these repetitive motions when, in the right context, are defensive karate techniques, which is the first step to learning karate, have to defend yourself. You can't go on the offensive if you can't protect yourself. And so this was a huge paradigm shift for Daniel, who you learned, oh, I was doing all this hard work, but that's how you could go to karate. Why do I share this story? Well, it's a great movie. You should check it out sometime. But this is exactly how many of us have felt in previous mathematics classes, like maybe pre-calculus or college algebra or high school algebra. We learn all of these algebraic tricks, and we practice them over and over and over, and they get repetitive, and they get tiresome, and we get fatigued from it. But like Daniel, we've been learning how to paint the fence and wax the car, but we were like, I want to learn karate. The good news is I'm going to be Mr. Miyagi. And in calculus one, we finally get to take those algebraic skills you've been rehearsing probably for years and apply them in the right context to solve some very useful real life problems. Calculus is sort of like the first step in approaching many, many mathematical problems we see in science, physics, chemistry, engineering, just to name a few things there. All right. And so because of that, those algebraic skills we've practiced in pre-calculus settings are really important. It's really the start of where we're going to do calculus. So the first chapter in our lecture series is going to be dedicated just to reviewing topics in pre-calculus, that is college algebra and trigonometry. And depending on you as the student will depend on how much review is actually necessary. Some of you came fresh out of college algebra, fresh out of trigonometry, and you're good to go. You have all these skills mastered, and for which the homework is just going to feel like busy work, just practicing things you already know. Many of you, on the other hand, maybe it's been a while since you've taken a pre-calculus class. Some of you haven't taken it since high school, which could be years. Some of them could be decades. It depends on the student, right? And that's OK. There's no judgment there. But some of us might be a little bit more atrophied in our algebra skills because it's been semesters or years or a long, long time. Even those who freshly came out of college algebra, maybe that was a hard class. And maybe we just need more practice anyways. And then with trigonometry, some high schools don't even teach trigonometry. And so some of you are going to thrown into this class with really no trigonometric background whatsoever. And so because of the sort of gap, huge gap for many of you in terms of prerequisites for this course, we're going to spend the first two weeks of our series learning, well, not learning, but reviewing college algebra and trigonometric things, reviewing all these topics. And so let me show you our first lecture page here. You're going to see several videos. And this is just the first lecture. You will go through several lectures, of course, throughout this series. But we see a couple of lectures here because some of us might not need as much practice as other. I have labeled some of the lecture videos differently. So now each lecture video, when you click on the tab, just click on it, it gives you a title, it gives you a description, it gives you the video which you can watch. This title and description is to help you with your notes also if you need a return to the videos in the future. So in this first chapter, chapter one on this review of pre-calculus, some of the videos I've labeled as optional. Because again, if you have taken college algebra and trigonometry, which if you got into this course you should have, because that's prerequisite. You've learned all of this stuff before. It really comes down to how much of a review do you actually need to do this class. It's hard to say, I don't actually know it, that that's sort of an individual thing for you. And so there are some things that I think are really essential that even if you're like the world expert on this, we probably should still review it. Those ones, you won't see any label there. There are some other topics which I think are worth reviewing, but many of us might not need a detailed review, in which case I'm labeling those as optional videos. So if you do feel like you have a stronger background in algebra, then by all means, you can skip the optional videos, not a big deal. I would still encourage you to watch the ones that are not labeled optional. Because again, some of them are optional, some of them are not. And then kind of go try to gauge yourself from there. Some of you who feel like you're gonna be the top national on students, like college algebra is never gonna be a problem for you, you might just jump straight in the homework and fall back onto the videos when you kind of get stuck. Like, oh, I don't remember how to do this. And that's okay for chapter one. Because like I said, chapter one, it's just gonna be a review of functions and trigonometry. When we get into chapter two and beyond, when we actually learn things that are new, things you shouldn't have seen before because they're properly calculus subjects, then I would encourage us to watch all of the videos in the order they're presented on Canvas before we begin the homework. But I will allow us to deviate from that strategy for this review chapter, which is chapter one. I should also mention that on every lecture, there's a link to lecture notes, the notes I use in a traditional face-to-face lecture, for which you can download those, read through these on your own if you would like to. If you want a very abbreviated run-through through the lectures, you could just read the lecture notes and get all the same stuff you get from the video as well. Now, I should also mention that the videos that we're gonna see in chapter one, were originally developed for my college algebra, math 1050 and trigonometry math 1060 courses. That's okay, I mean, the math didn't change as we review those things, but if you ever hear anything mentioned like, this is math 1050, well, that's just because the video was reused right there. And this is actually an advantage to us because while I've linked all of these videos on our lecture pages for your review, like I said, this is if you need sort of like the average review of materials. If you need a more in-depth review, which might be possible, that's not a big deal, no problem there whatsoever. If you need a little bit more review than what these videos are offering, then click the on-screen links you can see in the YouTube videos, like the one you see on the screen right now, and you can link into the entire library for math 1050 and you can scroll by topic and find anything you need to review as we go, not just for this review chapter, but anytime in the future, like, oh, I don't remember how to factor a quadratic polynomial. You might be surprised that maybe that needs to come up. You can always go back to the trigonometry or the college algebra lecture videos and take a look at those whenever you need that just-in-time practice.