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Precalculus: A View of the World Around Us, 1/e

David Wells, The Pennsylvania State University
Lynn Tilson, The Pennsylvania State University

Published January, 1998 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 727 pp.
Cloth
ISBN 0-02-425451-7


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Summary

Unique in perspective, this text supports innovative pedagogy and approach to precalculus mathematics—but does not require instructors to spend extensive time preparing to teach or to depart radically from the traditional course in either content or structure. Written in a student-friendly conversational style, it uses a variety of mathematical methods to investigate and solve both routine and non-routine real-world physical problems—showing students how mathematics can be used to “view the world around us.”

Features


Offers structural flexibility to enable instructors to adapt coverage to their own course preferences.
Presents mathematics using the “rule-of-four” by introducing concepts numerically, analytically, graphically, and verbally.

  • Helps students not only learn to represent relationships using equations, graphs, or tables, but to decide which representation is more appropriate to a given situation.
Emphasizes problem-solving skills.
  • Introduces Polya's four-step process in Ch. 1 and uses it consistently throughout.
  • Covers the most commonly used problem-solving strategies in Ch. 1 and uses them several times in each chapter.
Focuses on algebra as a pattern-seeking device that can lead to the discovery of underlying principles.
Explores functions dynamically.
  • Discusses where functions are increasing and decreasing and introduces the idea of average rate of change.
  • Foreshadows the idea of limit numerically and graphically.
Covers the use and application of graphing calculators where appropriate.
Intersperses Mathematical Looking Glasses throughout — to not only teach skills, but to create a curiosity and understanding of “the world around us.”
  • Presents a rich variety of situations involving real people and actual events showing mathematics as useful, timely, and interesting. Most show how mathematics can be applied to solve a physical problem, and some simply analyze a situation from a mathematical perspective.
Shows how mathematics is part of our historical heritage.
Features an abundance of exercises throughout which are:
  • Placed at strategic points within each section, as well as at the end of each section.
  • Based on the examples they follow — i.e., flow from concept to skill.
  • Identified according to purpose — creating models, interpreting mathematics, problem solving, writing to learn, making observations, review, extension.
  • Varied in nature — from drill to reflective.


Table of Contents
    1. Modeling and Problem Solving.
    2. Functions.
    3. Linear Systems.
    4. Quadratic Functions and Relations.
    5. Polynomial Functions.
    6. Rational Functions.
    7. Exponential and Logarithmic Functions.
    8. Trigonometric Functions.
    9. Trigonometric Functions as Analytical Tools.
    10. Trigonometric Functions as Graphing Tools.
    Appendix A: Basic Algebra Reference.
    Appendix B: Tips for Graphing Functions with A Calculator.


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