CALCULUS Understanding Its Concepts and Methods

*Calculus: Understanding Its Concepts
and Methods* is an electronic calculus textbook that
features live calculations and animated, manipulatable graphics.
Using the underlying framework of *Scientific Notebook, *the
book provides a dynamic environment for teaching and learning
calculus. This electronic textbook contains what is normally
taught in a three-semester calculus sequence. The explanatory
material is supplemented with examples and explorations, and
reinforced with problem sets and self tests.

The **index**
combines an index and a glossary. Each index entry links to a
glossary page that contains a brief definition of the entry. The
full glossary is available on this web site. In the book itself,
these glossary pages also link to pages in the text that provide
further explanation together with examples.

By applying the resources now available
through technology, *Calculus: Understanding Its Concepts and
Methods* provides easy access to relevant information and

enables a student to learn both basic concepts and computational details

provides a computer algebra system so that a student can explore, discover, and understand concepts

contains tools and hints that help an instructor facilitate learning and is a tool for classroom use, distance learning, and independent study

is
a complete calculus text and is also a useful supplement to any
other calculus text

*Calculus: Understanding Its Concepts
and Methods* provides a unique, dynamic setting for teaching
and learning calculus. Everything takes place in a unified *Scientific
Notebook *environment---a free-form easy-to-learn interface
to a computer algebra system integrated with a scientific word
processor. This allows students to experiment with the material,
solve interesting problems, and produce clear, well-written
homework. Live calculations, manipulatable graphics, and animated
plots enhance the presentation. Calculus concepts are made easier
to understand and students are encouraged to think like
mathematicians.

With *Scientific Notebook*,
mathematics is entered into a document using natural notation. It
can then be edited, evaluated, plotted, simplified, factored, and
expanded, without recourse to obscure programming syntax. The
output of the computer algebra system is also in natural notation
and is placed within the same document. Many different
mathematical forms are recognized, so the student is not required
to adhere to a single way of writing an expression. *Calculus:
Understanding Its Concepts and Methods* is composed of
thousands of read-only documents. Details of the construction of
graphs and formulas tend to be hidden, but any file can be saved
as a read-write document in which these details become
transparent. Everything produced in this book---2D and 3D
animations, translucent surfaces, formulas, etc.---can be
duplicated and modified by the reader.

How do mathematicians, engineers, and
scientists do mathematics? They observe patterns and make
conjectures as to what causes these patterns. When they solve a
particular problem, they use their solutions to solve related
problems. They test their solutions on verifiable special cases
and compare them with known results. They explain and justify
their solutions in words. This is the focus in *Calculus:
Understanding Its Concepts and Methods. *The *Scientific
Notebook* environment combines a computer-algebra system
with a word-processing system to support this approach to
mathematics. The skills developed using *Scientific Notebook*
will help students solve problems that they encounter in the
future because they will always be dealing with natural
mathematical notation and general problem-solving methods.

*Calculus: Understanding Its Concepts
and Methods* comprises the content normally taught in a
three-semester calculus sequence. The material is presented in a
way that encourages mathematical problem solving, experimentation,
exploration, and communication. It includes explanations,
examples, explorations, problem sets, self tests, and resource
information. Many of the files contain animations that the reader
can manipulate and control. Other files are interactive: you can
define your own function, or change some parameters, and observe
the results. This allows you to achieve important insights from
specific examples.

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.