The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein.

Well, I’m here to tell you that you can master calculus. It’s not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus. Read this jargon-free book, get a handle on calculus, and join the happy few who can proudly say, “Calculus? Oh, sure, I know calculus. It’s no big deal.”

About This Book

Calculus Essentials For Dummies is intended for three groups of readers: students taking their first calculus course, students who need to brush up on their calculus to prepare for other studies, and adults of all ages who’d like a good introduction to the subject. For those who’d like a fuller treatment of the subject, check out Calculus For Dummies.

If you’re enrolled in a calculus course and you find your textbook less than crystal clear, Calculus Essentials For Dummies is the book for you. It covers the two most important topics in the first year of calculus: differentiation and integration.

If you’ve had elementary calculus, but it’s been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus Essentials For Dummies will give you a quick, no-nonsense refresher course.

Nonstudent readers will find the book’s exposition clear and accessible. Calculus Essentials For Dummies takes calculus out of the ivory tower and brings it down to earth.

This is a user-friendly math book. Whenever possible, I explain the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. I then show you how the calculus concepts work in concrete examples. Only later do I give you the fancy calculus formulas. All explanations are in plain English, not math-speak.

Conventions Used in This Book

The following conventions keep the text consistent and oh-so-easy to follow.

• Variables are in italics.
• Calculus terms are italicized and defined when they first appear in the text.
• In the step-by-step problem-solving methods, the general action you need to take is in bold, followed by the specifics of the particular problem.

Foolish Assumptions

Call me crazy, but I assume …

• You know at least the basics of algebra, geometry, and trig.

• If you’re rusty, you might want to brush up a bit on these pre-calculus topics. Actually, if you’re not currently taking a calculus course, and you’re reading this book just to satisfy a general curiosity about calculus, you can get a good conceptual picture of the subject without the nitty-gritty details of algebra, geometry, and trig. But you won’t, in that case, be able to follow all the problem solutions. In short, without the pre-calculus stuff, you can see the calculus forest, but not the trees. If you are enrolled in a calculus course, you’ve got no choice — you’ve got to know the trees.

• You’re willing to do some w_ _ _.

• No, not the dreaded w-word! Yes, that’s w-o-r-k, work. I’ve tried to make this material as accessible as possible, but it is calculus after all. You can’t learn calculus by just listening to a tape in your car or taking a pill — not yet anyway.

Icons Used in This Book

Keep your eyes on the icons:

Next to this icon are the essential calculus rules, definitions, and formulas you should definitely know.

These are things you need to know from algebra, geometry, or trig, or things you should recall from earlier in the book.

The bull’s-eye icon appears next to things that will make your life easier. Take note.

This icon highlights common calculus mistakes. Take heed.

In contrast to the Critical Calculus Concepts, you generally don’t need to memorize the fancy-pants formulas next to this icon unless your calc teacher insists.

Where to Go from Here

Why, Chapter 1, of course, if you want to start at the beginning. If you already have some background in calculus or just need a refresher course in one area or another, then feel free to skip around. Use the table of contents and index to find what you’re looking for. If all goes well, in a half a year or so, you’ll be able to check calculus off your bucket list:

• ___ Run a marathon
• ___ Go skydiving
• ___ Write a book
•  x Learn calculus
• ___ Swim the English Channel
• ___ Cure cancer
• ___ Write a symphony
• ___ Pull an inverted 360° at the X-Games

For the rest of your list, you’re on your own.