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

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To the Student

This College Algebra 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 a 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

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