Next: A last note
Calculus from Graphical, Numerical, and Symbolic
Points of View
Arnold Ostebee and Paul Zorn, St. Olaf College
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.
In short: read the book.
- 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.
Next: A last note
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