Hi! And welcome to the Calculus 1 video tutor. The purpose of this DVD course is to teach you about Calculus obviously. The way we are going to that is we are going to work is we are going to work is we are going to work a lot of example problems in each and every section.
Before we get into that stuff, I just want to give you my two minutes speech on Calculus and why it is important. First thing, I want to really say first rule, put all of your fears aside, okay?
Calculus has it bad reputation, it is something really hard to understand, something really complicated because gee they named is Calculus. I mean, Calculus just sounds me, okay?
So, I want you to take those thoughts. I want you to put them on the back burden because they are not true. I am going to teach you how to do Calculus, and it is going to seem like third grade math, that is my goal, okay?
My goal is to work every step, step by step by step and to do enough problem, so that you will comfortable doing them on your own. And the goal is that getting that experience will help you go into your homework, and then do your test, and do well right after that.
Now, the other thing I wanted to say is I am not going to work problems of every type. I am not going to cover every single topic that you might cover in class. So, what you are going to need to be willing to do on your end is to pick up the book and to look additional problems. I promise you, I have tutored a lot of people in this subject, and in other subjects in math. And, really the way you do it is just like football or hockey, or soccer, you have to practice it, okay?
So, I will do my part. I will teach you that the shortcuts, I will not say it is the shortcuts but the quick and the straight truth on how to do the problems. I am not going to have a lot of theory. I am going to explain what I need to explain to you. Mainly, I am going to show you how to do it by working examples. So, watch the DVD course from beginning to the end, and I promise you that if you that, and if you make sure you understand what I am talking about before I go on then we will be in good shape.
Okay, so let us move in to the topic of this particular section of the class. The first section, which is the concept of the derivative, okay? There are two main things that you have to learn in calculus 1, if you just have to boil them down.
The first one is called the derivative and we are going to devote the next several sections to that. And then, the second topic really is called an interval, and they have goofy, really scary sounding names, okay?
But, I am just telling you what a derivative is. I want to show you what a derivative is, so let me try to that.
Let us say this pen here is moving along in a constant speed like this. It is not speeding up, you know, it is not slowing down, it is just marching across your field of view like this at a constant speed, okay? So, if we were doing this, okay? And if you are in your car and it will going long like this, then you would say it will be going like on a like 10 mile an hour constantly. The speed is 10 miles and hour, okay? So, it goes across constantly.
So, if we were to plot the position of this pen as a function of time, what would it look like? If we did that, we have a graph like this, and this would be time, and this would be position. I am going to say POS for position, okay? And then along this axis you will have a little tick marks for time, one second, two second, three seconds, four seconds, so long. And then, on this axis, you will have you know, your distance. You know, how far away have you gone from the origin, okay? So, this could be like one feet, and one foot, two foot, three foot, and so on.
So, if this pen is going a long your field of view in a constant rate, what would this graph look like? I think you can convince your self that this graph is going to look like a straight line, because each unit of time that I go forward, it goes forward in position every time I go one second it goes up the same amount in the position. So, as I go forward in time, it goes for
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