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Product No. 7671 Textbook Price: $88.00
 

College Algebra: Modeling Our World 1si Edition 2018 CD-Rom ( Teachers Edition )

Nancy Crisler & Gary Froelich

Mathematics Topic:
Algebra, Modeling, Precalculus
Application Areas:
Various

| ©2018 by COMAP, Inc. | 1st Edition | ISBN: 978-1-933223-57-5 |



Click here to view the Student Edition.

To the Teacher

Since its inception in 1980, COMAP has been dedicated to presenting mathematics through contemporary applications. We have produced high school and college texts, hundreds of supplemental modules, and three television courses—all with the purpose of showing students how mathematics is used in their daily lives. College Algebra: Modeling Our World is a text rooted in the COMAP philosophy.

The word "modeling" is the key. Real problems do not come at the end of chapters. Real problems don't look like mathematics problems. Real problems are messy. Real problems ask questions such as: How do we create computer animation? How do we effectively control an animal population? What is the best location for a fire station? What do we mean by "best"?

Mathematical modeling is the process of looking at a situation, formulating a problem, finding a mathematical core, working within that core, and coming back to see what mathematics tells us about the original problem. We do not know in advance what mathematics to apply. The mathematics we settle on may be a mix of geometry, algebra, trigonometry, data analysis, and probability. We may need to use computers or graphing calculators, spreadsheets, or other utilities. At heart, we want to demonstrate to students that mathematics is the most useful subject they will learn. More importantly, we hope to demonstrate that using mathematics to solve interesting problems about how our world works can be a truly enjoyable and rewarding experience. Ultimately, learning to model is learning to learn.

Yes, the text makes extensive use of technology. Yes, the text is activity-based. And, of course, the text is applications and modeling driven. But, make no mistake. This is a serious precalculus text. We emphasize that mathematics as a discipline has a structure of its own, and that as students go on into the study of mathematics they will learn more and more of that structure and the power it provides to solve an amazingly wide array of problems.

This course is the gateway to collegiate mathematics. As such, students will see a number of essential new concepts and be asked to learn a number of important new skills And we believe that the material in this text can provide students with a firm background for any entry-level undergraduate mathematics course—continuous or discrete. For example, we have provided substantial material on matrices and vectors as well as a full chapter on discrete dynamical systems. We believe that the treatment of these topics will prepare students for a deeper understanding of the concepts underlying the calculus as well as those underlying discrete mathematical structures.

What you will find here is a challenging pre-calculus course. And, in the COMAP tradition, you will find exciting, contemporary applications and models presented in novel ways to help teach and motivate the further study of our discipline.

Solomon Garfunkel
EXECUTIVE DIRECTOR, COMAP

Table of Contents:

CHAPTER 1
Functions in Modeling

  • LESSON 1.1: Functions as Models
  • LESSON 1.2: Creating a Mathematical Model
  • LESSON 1.3: Modeling Linear Patterns: Beginning the Tool Kit of Functions
  • LESSON 1.4: Expanding the Tool Kit of Functions
  • LESSON 1.5: Transformations of Functions
  • LESSON 1.6: Operations on Functions
  • CHAPTER 1 REVIEW

    CHAPTER 2
    The Exponential and Logarithmic Functions

  • LESSON 2.1: Exponential Functions
  • LESSON 2.2: Logarithmic Scale
  • LESSON 2.3: Changing Bases
  • LESSON 2.4: Logarithmic Functions
  • LESSON 2.5: Modeling with Exponential and Logarithmic Functions
  • LESSON 2.6: Composition and Inverses of Functions
  • CHAPTER 2 REVIEW

    CHAPTER 3
    Polynomial Models

  • LESSON 3.1: Modeling Falling Objects
  • LESSON 3.2: The Merits of Polynomial Models
  • LESSON 3.3: The Power of Polynomials
  • LESSON 3.4: Zeroing in on Polynomials
  • LESSON 3.5: Polynomial Divisions
  • LESSON 3.6: Polynomial Approximations
  • CHAPTER 3 REVIEW

    CHAPTER 4
    Matrices

  • LESSON 4.1: Matrix Basics
  • LESSON 4.2: The Multiplicative Inverse
  • LESSON 4.3: Systems of Equations in Three Variables
  • CHAPTER 4 REVIEW

    CHAPTER 5
    Analytic Geometry

  • LESSON 5.1: Analytic Geometry and Loci
  • LESSON 5.2: Modeling with Circles
  • LESSON 5.3: Modeling with Parabolas
  • LESSON 5.4: Modeling with Ellipses
  • LESSON 5.5: Modeling with Hyperbolas
  • CHAPTER 5 REVIEW

    CHAPTER 6
    Counting and the Binomial Theorem

  • LESSON 6.1: Counting Basics
  • LESSON 6.2: Compound Events
  • LESSON 6.3: The Binomial Theorem
  • CHAPTER 6 REVIEW

    APPENDICES A–H
    APPENDICES SOLUTIONS
    CALCULATOR APPENDICES A–K
    INDEX

    Teacher’s Guide

    Teacher’s Resources

  • Handouts
  • Assessment Problems
  • Transparencies
  • Software
  • Solutions Manual
  • Supplemental Activities