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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
