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Calculus Primer 1: Introduction
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Copyright © 2004, P. Lutus

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I wish Calculus had a better name. Isaac Newton, one of the people responsible for inventing it, called it "fluxions." That name might alleviate one of the primary obstacles to learning Calculus — people hear the name and experience pure fear. In fact, I understand one may not yell "Calculus" in a crowded theater without risking arrest.

I think Calculus knowledge is a right, not a privilege, and I think it's a shame most people in the U.S. never learn it. That's why I wrote these pages — Calculus is a part of life, it describes things in a way no other kind of mathematics can, and it's interesting.

Calculus has a property in common with many other skills in life — it is a bit more complicated than picking up a rock. As a result of this, the usual gaggle of self-important drones gather near it, genuflect toward it reverently, and tell you it is too complicated for your minuscule brain. They don't tell you Calculus is an enriching addition to your personal intellectual toolkit — that is not in their interest. Above all, they don't tell you ... it's fun.

"Fun"? On reading this you may wonder what I've been smoking. You may have been exposed to Calculus in school — or, worse, told that you weren't cut out for it — so you missed discovering what separates it from other kinds of mathematics — in Calculus, things start moving.

To return to something I said earlier, why is Calculus different than picking up a rock? Well, if you pick up a rock and hold it in your hand, you can make a statement about the rock's weight or its color. You can even make a mathematical statement about the relationship between the rock and the Earth, how the two masses are attracted toward each other. You can do all that with algebra and a little physics.

But to discover why Calculus is important, try dropping the rock. As the rock begins to fall, it leaves the domain of algebra and enters the domain of Calculus, because Calculus is the mathematics of motion and change.

How much force does the rock experience by being attracted by the Earth? How fast is it moving? Does it move faster as time passes? How long will it take to get to the ground? All the answers are provided by Calculus.

It is said that Isaac Newton watched an apple fall from a tree and asked these same questions. He thought up a way to describe the apple's fall, then he looked above the tree and wondered if the same rules might not apply to the moon as well. He created a new, powerful tool for thinking about the world and the universe.

Don't be cheated out of an enriching experience — make Calculus your tool as well.

This primer presents the broad outline of Calculus. It is meant only as an introduction to the subject. It provides a sense of the topic without many of the details and techniques that a more complete treatment would provide.

Nevertheless, to be able to follow these pages, you will need to know some algebra and have a conception of what a mathematical function is (these pages will help you understand functions). It is best if you can peruse these pages without being distracted, at a time when you are rested and in the mood for an adventure.

This tutorial is only the briefest overview of a fascinating topic. It is the author's hope that these pages will inspire you to learn Calculus in much greater depth.

To navigate this tutorial, choose topics from the drop-down lists at the top and bottom of this page, or click the arrow symbols to move through the pages sequentially.


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