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Calculus is the study of change in motion, and it's increasingly utilized today in fields not only like physics and chemistry, but also finance, business, ecology, statistics, and even video game design.
The purpose of the course is to help you to prepare for either the AB or BC calculus course. We will do this by previewing some of the big ideas of calculus and also reviewing some ideas from algebra that will help you to do this.
This course is organized into the following sections:
We'll present the material in a variety of ways, but the most important of the practice activities and exercises in each lesson. Try the problems without looking at the answer first, see what you get, and then compare your answer with ours. If it's not the same check your work for a mistake and try it again. If you still can't get it, then it's time to look at the answer and the complete explanation of each problem which we give you. Study the explanation and then try another problem. You need to be an active participant in your mathematical education, and this class will give you many opportunities to do just that.
Wow, that sure looks like a fun ride. Is there any way to include that in our calculus course somehow? Well, calculus is the study of change in motion. When an object is in motion like the roller coaster, a lot of things are changing- your velocity, your position, your height above the ground, the distance that you traveled. Maybe even your heart rate and your blood pressure. So many of those quantities are changing, we're just going to focus on one of those quantities, the height that the rider is above the ground. Sometimes the rider's height is changing very slowly, but sometimes it's changing rapidly. Sometimes the rider's moving up, which we'll call a positive change, and sometimes moving down, which we'll call a negative change. And so that leads us to the question, at a given moment how is the rider's height above the ground changing? In the real world, we can't stop a roller coaster when we want to measure the rate of change. But we can do something somewhat similar mathematically. So let's get more comfortable with the concept of average rates of change. And to do this, click on the roller coaster graph.
