cbicon.png CALCULUS Understanding Its Concepts and Methods

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Preface

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

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          $enables a student to learn both basic concepts and computational details

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

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

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          $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.

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