About this book: notes for students

All authors want their books to be used: read, studied, thought about, puzzled over, reread, underlined, disputed, understood, and, ultimately, enjoyed. So do we.

That might go without saying for some books-beach novels, user manuals, field guides, etc.-but it may need repeating for a calculus textbook. We know as teachers (and remember as students) that mathematics textbooks are too often read backwards: faced with Exercise 231(b) on page 1638, we've all shuffled backwards through the pages in search of something similar. (Very often, moreover, our searches were rewarded.)

A calculus textbook isn't a novel. It's a peculiar hybrid of encyclopedia, dictionary, atlas, anthology, daily newspaper, shop manual, and novel-not exactly light reading, but essential reading nevertheless. Ideally, a calculus book should be read in all directions: left to right, top to bottom, back to front, and even front to back. That's a tall order. Here are some suggestions for coping with it.

Read the narrative.

Each section's narrative is designed to be read from beginning to end. The examples, in particular, are supposed to illustrate ideas and make them concrete-not just serve as templates for homework exercises.

Read the examples.

Examples are, if anything, more important than theorems, remarks, and other ``talk.'' We use examples both to show already-familiar calculus ideas ``in action,'' and to set the stage for new ideas.

Read the pictures.

We're serious about the ``graphical points of view'' mentioned in our title. The pictures in this book are not ``illustrations'' or ``decorations.'' Pictures are everywhere in this book, even in the middle of sentences. That's intentional: graphs are an important part of the language of calculus. An ability to think ``pictorially''-as well as symbolically and numerically-about mathematical ideas may be the most important benefit calculus can offer.

Read with a calculator and pencil.

This book is full of requestsOften they're put in margin notes, like this one. to check a calculation, sketch a graph, or ``convince yourself'' that something makes sense. Take these ``requests'' seriously. Mastering mathematical ideas takes more than reading; it takes doing, drawing, and thinking.

Read the language.

Mathematics is not a ``natural language'' like English or French, but it has its own vocabulary and usage rules. Calculus, especially, relies on careful use of technical language. Words like rate, amount, concave, stationary point, and root have precise, agreed-upon mathematical meanings. Understanding such words goes a long way toward understanding the mathematics they convey; misunderstanding the words leads inevitably to confusion. Whenever in doubt, consult the index.

Read the appendices.

The human appendix generally lies unnoticed-unless trouble starts, when it's taken out and thrown away. Don't treat our appendices that way. Though perhaps slightly enlarged, they're full of healthy matter: reviews of precalculus topics, help with ``story problems,'' proofs of various kinds, even a graphical ``atlas'' of functions. Used as directed the appendices will help appreciably in digesting the material.

Read the instructors' preface (if you like).

Get a jump on your teacher.

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