Calculus For Dummies, 2nd Edition (2014)

Introduction

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.

But why should you bother — apart from being required to take a course? Why climb Mt. Everest? Why listen to Beethoven’s Ninth Symphony? Why visit the Louvre to see the Mona Lisa? Why watch South Park? Like these endeavors, doing calculus can be its own reward. There are many who say that calculus is one of the crowning achievements in all of intellectual history. As such, it’s worth the effort. 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 For Dummies, 2nd Edition, 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.

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

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 For Dummies, 2nd Edition will give you a thorough, no-nonsense refresher course.

Non-student readers will find the book’s exposition clear and accessible. Calculus For Dummies, 2nd Edition, 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.

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.

It can be a great aid to true understanding of calculus — or any math topic for that matter — to focus on the why in addition to the how-to. With this in mind, I’ve put a lot of effort into explaining the underlying logic of many of the ideas in this book. If you want to give your study of calculus a solid foundation, you should read these explanations. But if you’re really in a hurry, you can cut to the chase and read only the important introductory stuff, the example problems, the step-by-step solutions, and all the rules and definitions next to the icons. You can then read the remaining exposition only if you feel the need.

I find the sidebars interesting and entertaining. (What do you expect? I wrote them!) But you can skip them without missing any essential calculus. No, you won’t be tested on this stuff.

Minor note: Within this book, you may note that some web addresses break across two lines of text. If you’re reading this book in print and want to visit one of these web pages, simply key in the web address exactly as it’s noted in the text, as though the line break doesn’t exist. If you’re reading this as an e-book, you’ve got it easy — just click the web address to be taken directly to the web page.

Foolish Assumptions

Call me crazy, but I assume …

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

If you’re rusty, Part 2 (and the online Cheat Sheet) contains a good review of 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’re enrolled in a calculus course, you’ve got no choice — you’ve got to know the trees as well as the forest.

· 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.

Is that too much to ask?

Icons Used in This Book

Keep your eyes on the icons:

Next to this icon are calculus rules, definitions, and formulas.

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.

Beyond the Book

There’s some great supplementary calculus material online that you might want to check out:

· To view this book’s Cheat Sheet, simply go to www.dummies.com and search for “Calculus For Dummies Cheat Sheet” in the Search box; you’ll find a nice list of important formulas, theorems, definitions, and so on from algebra, geometry, trigonometry, and calculus. This is a great place to go if you forget a formula.

· At www.dummies.com, there are articles on some calculus topics that many calculus courses skip. For example, the online article “Finding Volume with the Matryoshka Doll Method (a.k.a. the Cylindrical Shell Method)” covers one of the methods for computing volume that used to be part of the standard calculus curriculum, but which is now often omitted. You’ll also find other interesting, off-the-beaten-path calculus articles. Check them out if you just can’t get enough calculus.

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 list:

· ___ Run a marathon

· ___ Go skydiving

· ___ Write a book

·  Learn calculus

· ___ Swim the English Channel

· ___ Cure cancer

· ___ Write a symphony

· ___Pull an inverted 720° at the X-Games

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