Precalculus: Graphing and Data Analysis

Precalculus: Graphing and Data Analysis, 1/e

Michael Sullivan, Chicago State University
Michael Sullivan, South Suburban College

Published December, 1997 by Prentice Hall Engineering/Science/Mathematics

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Precalculus with Graphing Calculators-Mathematics

Summary

Designed for the Precalculus course covering algebra and trigonometry. This text covers unit circle trigonometry first and then explores the right angle approach. This text requires student use of graphing calculators or a computer based software program. For schools who wish to cover right angle first, please see “Algebra and Trigonometry: Graphing and Data Analysis”. The goal of this text is to provide a solid mathematical foundation via visualization of real world data. Technology is used as a tool to solve problems, motivate concepts, explore and preview mathematical concepts and to find curves of best fit to the data. Most mathematical concepts are developed and illustrated both algebraically and graphically - with the more intuitive and appropriate method presented first. Also included in this text is a foreshadowing of calculus through the chapter on Limits and Derivatives.

Features

@BREAKNOLINALT = Mathematics
The authors use their extensive teaching and writing experiences to guide and support students through the typical difficult areas.
Each section opens with the mathematical objectives of the section. Each objective is referenced as it is encountered in the section.
Examples are worked out step-by-step, both numerically and in “English”.
Many examples include the “Now Work” feature which suggests a similar odd-numbered problem from the section exercise set. This allows for immediate reinforcement of concepts through doing.
“Historical Notes” are provided in context, enhancing student interest, provide anecdotal information on how and where mathematical concepts have come from.
Exercises are carefully crafted — beginning with confidence builders and visualization exercises, then practice and drill, followed by the more challenging and application driven problems. Discussion, Writing and Research questions are clearly called out by the red icon in the margin.
Each chapter opens by listing the concepts (and page references) that the student will need to review “Before Getting Started”.
The chapters conclude with a detailed chapter review, including “Important Formulas, Theorems and Definitions”, a list of “Things to Know and Do”, True/False Questions, Fill-in-the-Blank items, and Review Exercises. @BREAKNOLINALT = Technology
The authors approach the use of technology as an enhancement to the learning of mathematics not as a replacement for learning.
Graphing utilities are used to help students analyze data and find curves of best fit. Types of curve fitting discussed include: linear, quadratic, cubic, power, exponential, logarithmic, logistic, and sinusoidal.
Using the power of the grapher, students are able to approach problems and concepts that may have been beyond them without the grapher.
Real TI-83 screen shots are used as the illustrations for the purpose of clear visualization of the materials. @BREAKNOLINALT = Data
Sourced data connects the mathematical concepts to other disciplines and other interests of the students - adding relevancy and motivation.
Applications involving data analysis utilize real world sources such as the US Census Bureau, Government Agencies and the Internet.
Each chapter has an “Internet Exploration”. These optional explorations introduce students to “live data” via the Internet. Multiple questions follow each exploration encouraging the use of Polya's problem solving strategies. The links to the sites are all maintained via the Prentice Hall Companion Website for Sullivan at
www.prenhall.com/sullivan

Table of Contents

1. Graphs and Equations.
2. Functions and Their Graphs.
3. Polynomial and Rational Functions.
4. Exponential and Logarithmic Functions.
5. Trigonometric Functions.
6. Analytic Trigonometry.
7. Applications of Trigonometric Functions.
8. Polar Coordinates; Vectors.
9. Analytic Geometry.
10. Systems of Equations and Inequalities.
11. Sequence; Induction; Counting; Probability.
12. A Preview of Calculus: The Limit and the Derivative of a Function.
Appendix: Review.
Answers.
Index.