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Product No. 7629 Textbook Price: $54.00
 

Precalculus: Modeling Our World 1st Edition CD-Rom ( Student Edition )

Nancy Crisler, Gary Froelich

Mathematics Topic:
Precalculus
Application Areas:
Various

©2002 by COMAP, Inc.


Click here to view the Teacher's Edition.

Dear Student,

This Precalculus text is a different kind of math book than you may have used, for a different kind of math course than you may have taken. In addition to presenting mathematics for you to learn, we have tried to present mathematics for you to use. We have attempted in this text to demonstrate mathematical concepts in the context of how they are actually used day to day. The word "modeling" is the key. Real problems do not come at the end of chapters in a math book. Real problems don't look like math problems. Real problems ask questions such as: How do we create computer animations? Where should we locate a fire station? How do we effectively control an animal population? Real problems are messy.

Mathematical modeling is the process of looking at a problem, finding a mathematical core, working within that core, and coming back to see what mathematics tells you about the problem with which you started. You will not necessarily know in advance what mathematics to apply. The mathematics you settle on may be a mix of several ideas in geometry, algebra, and data analysis. You may need to use computers or graphing calculators. Because we bring to bear many different mathematical ideas as well as technologies, we call our approach "integrated."

Another very important and very real feature of this course is that frequently you will be working in groups. Many problems will be solved more efficiently by people working in teams. We have done all of this to emphasize our primary goal: Presenting you with mathematical ideas the way you will see them as you go on in school and out into the work force. There is hardly a career that you can think of in which mathematics will not play an important part and in which understanding mathematics will not matter to you.

This course is the gateway to collegiate mathematics. As such you will see a number of essential new concepts and be asked to learn a number of important new skills. But, most of all, we hope you have fun. Mathematics is important. Mathematics may be the most useful subject you will learn. Using mathematics to solve truly interesting problems about how our world works can and should be an enjoyable and rewarding experience.

Solomon Garfunkel
EXECUTIVE DIRECTOR, COMAP

CHAPTER 1
Functions in Modeling

  • Introduction
  • 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 4
    Trigonometric Functions

  • LESSON 4.1 Oscillating Phenomena and Periodic Functions
  • LESSON 4.2 The Sine Function
  • LESSON 4.3 The Cosine Function
  • LESSON 4.4 The Tangent and Other Functions

    CHAPTER 5
    Triangle Trigonometry

  • LESSON 5.1 Right Triangles
  • LESSON 5.2 Inverses
  • LESSON 5.3 Oblique Triangles

    CHAPTER 6
    Coordinate Systems and Vectors

  • LESSON 6.1 Polar Coordinates
  • LESSON 6.2 Polar Form of Complex Numbers
  • LESSON 6.3 The Geometry of Vectors
  • LESSON 6.4 The Algebra of Vectors
  • LESSON 6.5 Vector and Parametric Equations in Two Dimensions
  • LESSON 6.6 Vector Equations in Three Dimensions
  • CHAPTER 6 REVIEW

    CHAPTER 7
    Matrices

  • LESSON 7.1 Matrix Basics
  • LESSON 7.2 The Multiplicative Inverse
  • LESSON 7.3 Systems of Equations in Three Variables

    CHAPTER 8
    Analytic Geometry

  • LESSON 8.1 Analytic Geometry and Loci
  • LESSON 8.2 Modeling with Circles
  • LESSON 8.3 Modeling with Parabolas
  • LESSON 8.4 Modeling with Ellipses
  • LESSON 8.5 Modeling with Hyperbolas
  • CHAPTER 8 REVIEW

    CHAPTER 9
    Counting and the Binomial Theorem

  • LESSON 9.1 Counting Basics
  • LESSON 9.2 Compound Events
  • LESSON 9.3 The Binomial Theorem

    CHAPTER 10
    Modeling Change with Discrete Dynamical Systems

  • LESSON 10.1 Modeling Change with Difference Equations
  • LESSON 10.2 Approximating Change with Difference Equations
  • LESSON 10.3 Numerical Solutions
  • LESSON 10.4 Systems of Difference Equations