Christopher Monahan - Idiots Guides: Calculus II

No one likes a know-it-all. Most of us realize theres no such thinghow could there be? The world is far too complicated for someone to understand everything there is to know. So when you come across a know-it-all, you smile to yourself as they ramble on because you know better.

You understand that the quest for knowledge is a never-ending one, and youre okay with that. You have no desire to know everything, just the next thing. You know what you dont know, youre confident enough to admit it, and youre motivated to do something about it.

At Idiots Guides, we, too, know what we dont know, and we make it our business to find out. We find really smart people who are experts in their fields and then we roll up our sleeves and get to work, asking lots of questions and thinking long and hard about how best to pass along their knowledge to you in the easiest, most-accessible way possible.

After all, thats our promiseto make whatever you want to learn As Easy as It Gets. That means giving you a well-organized design that seamlessly and effortlessly guides you from page to page, topic to topic. It means controlling the pace youre asked to absorb new informationnot too much at once but just what you need to know right now. It means giving you a clear progression from easy to more difficult. It means giving you more instructional steps wherever necessary to really explain the details. And it means giving you fewer words and more illustrations wherever its better to show rather than tell.

So here you are, at the start of something new. The next chapter in your quest. It can be an intimidating place to be, but youve been here before and so have we. Clear your mind and turn the page. By the end of this book, you wont be a know-it-all, but your world will be a little less complicated than it was before. And well be sure your journey is as easy as it gets.

Mike Sanders
Publisher, Idiots Guides

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First American Edition, 2016
Published in the United States by DK Publishing
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ISBN: 9781465454409
Library of Congress Catalog Card Number: 2016941029

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This book is dedicated to one very special woman, my wife, Diane. Her encouragement throughout this process was always appreciated.

Contents

Introduction

If you look up the word calculus in the dictionary, one of the first definitions given is that it is a hard object, like a kidney stone. People used to joke that it was no wonder that the subject was so difficult to pass. This book is intended to soften the calculus so you are able to better understand Calculus II.

I have tried to avoid using the technical language of mathematics whenever I could. When I absolutely had to use more technical language, I have translated those terms into everyday language you can comprehend. Also, youll find plenty of examples in each chapter to help you understand the solutions to each problem. These examples include easy-to-understand explanations as well as the requisite mathematical notations.

However, I warn you not to be a mathematical voyeur, one who likes to watch the math being done but who does not do it himself. As you are working through this book, be sure to have paper, pencil, and your graphing calculator by your sideand use them. Read the example, do the problem yourself, then look at my solution. You might want to hide the example solutions before you do the problem so you cannot cheat. People who have taken calculus will tell you that the first step in the problem is calculus, but the rest of the steps needed to solve the problem are algebra. Be careful as you work.

Not every example problem included is easy. If I took that approach to teaching Calculus II, I would be giving you a false sense of what to expect. Making things too easy also would deny you the satisfaction of taking on a challenge and succeeding.

Finally, I used to tell my students to have fun when I handed them their exams. Your first reaction to that might be similar to their reactionsWise a**! However, I hope that after reading this book, you will come to understandas my students didlearning Calculus II is a chance to show yourself what you can do when you set your mind to it and have fun with this book. You never know what you can do until you try.

How This Book Is Organized

This book is presented in four parts:

In , Review of Pre-Calculus and Calculus I, you review a few key topics that you covered in Pre-Calculus and come into play in Calculus II. Youll also do a quick review of limits and derivatives from Calculus I.