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Precalculus Through Modeling and Visualization

Precalculus Through Modeling and Visualization - 3rd edition

ISBN13: 978-0321279071

Cover of Precalculus Through Modeling and Visualization 3RD 06 (ISBN 978-0321279071)
ISBN13: 978-0321279071
ISBN10: 0321279077
Cover type: Hardback
Edition/Copyright: 3RD 06
Publisher: Addison-Wesley Longman, Inc.
Published: 2006
International: No

List price: $176.00

Precalculus Through Modeling and Visualization - 3RD 06 edition

ISBN13: 978-0321279071

Gary K. Rockswold

ISBN13: 978-0321279071
ISBN10: 0321279077
Cover type: Hardback
Edition/Copyright: 3RD 06
Publisher: Addison-Wesley Longman, Inc.

Published: 2006
International: No
Summary

Gary Rockswold focuses on teaching algebra in context, answering the question, ''Why am I learning this?'' and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

Table of Contents

Chapter 1: INTRODUCTION TO FUNCTIONS AND GRAPHS

1.1 Numbers, Data, and Problem Solving

Sets of Numbers

Scientific Notation

Problem Solving

1.2 Visualization of Data

One-Variable Data

Two Variable Data

The Distance Formula

The Midpoint Formula

Graphing with a Calculator (Optional)

Checking Basic Concepts for Sections 1.1 and 1.2

1.3 Functions and Their Representations

Basic Concepts

Representations of Functions

FormalDefinition of a Function

Graphing Calculators and Functions (Optional)

Identifying Functions

1.4 Types of Functions and Their Rates of Change

Constant Functions

Linear Functions

Slope as a Rate of Change

Nonlinear Functions

Average Rate of Change

The Difference Quotient

Checking Basic Concepts for Sections 1.3 and 1.4

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Extended and Discovery Exercises

Chapter 2: LINEAR FUNCTIONS AND EQUATIONS

2.1 Linear Functions and Models

Exact and Approximate Models

Representations of Linear Functions

Modeling with Linear Functions

Linear Regression (Optional)

2.2 Equations of Lines

Forms for Equations of Lines

Determining Intercepts

Horizontal, Vertical, Parallel, and Perpendicular Lines

Modeling Data (Optional)

Interpolation and Extrapolation

Direct Variation

Checking Basic Concepts for Sections 2.1 and 2.2

2.3 Linear Equations

Equations

Symbolic Solutions

Graphical and Numerical Solutions

Problem-Solving Strategies

2.4 Linear Inequalities

Inequalities

Interval Notion

Techniques for Solving Inequalities

Compound Inequalities

Checking Basic Concepts for Sections 2.3 and 2.4

2.5 Piecewise-Defined Functions

Evaluating and Graphing Piecewise-Defined Functions

The Greatest Integer Function

The Absolute Value Function

Equations and Inequalities Involving Absolute Values

Checking Basic Concepts for Section 2.5

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Extended and Discovery Exercises

Chapter 1-2 Cumulative Review Exercises

Chapter 3: QUADRATIC FUNCTIONS AND EQUATIONS

3.1 Quadratic Functions and Models

Basic Concepts

Completing the Square and the Vertex Formula

Applications and Models

Quadratic Regression (Optional)

3.2 Quadratic Equations and Problem Solving

Basic Concepts

Solving Quadratic Equations

Problem Solving

Checking Basic Concepts for Sections 3.1 and 3.2

3.3 Quadratic Inequalities

Graphical Solutions

Symbolic Solutions

3.4 Transformations of Graphs

Vertical and Horizontal Translations

Stretching and Shrinking

Reflection of Graphs

Combining Transformations

Modeling with Transformations (Optional)

Checking Basic Concepts for Sections 3.3 and 3.4

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Extended and Discovery Exercises

Chapter 4: NONLINEAR FUNCTIONS AND EQUATIONS

4.1 Nonlinear Functions and Their Graphs

Polynomial Functions

Increasing and Decreasing Functions

Extrema of Nonlinear Functions

Symmetry

4.2 Polynomial Functions and Models

Graphs of Polynomial Functions

Piecewise-Defined Polynomial Functions

Polynomial Regression (Optional)

Checking Basic Concepts for Sections 4.1 and 4.2

4.3 Real Zeros of Polynomial Functions

Division of Polynomials

Factoring Polynomials

Graphs and Multiple Zeros

Rational Zeros

Polynomial Equations

4.4 The Fundamental Theorem of Algebra

Complex Numbers

Quadratic Equations with Complex Solutions

Fundamental Theorem of Algebra

Polynomial Equations with Complex Solutions

Checking Basic Concepts for Sections 4.3 and 4.4

4.5 Rational Functions and Models

Rational Functions

Vertical Asymptotes

Horizontal Asymptotes

Identifying Asymptotes

Rational Equations

Variation

4.6 Polynomial and Rational Inequalities

Polynomial Inequalities

Rational Inequalities

Checking Basic Concepts for Sections 4.5 and 4.6

4.7 Power Functions and Radical Equations

Rational Exponents and Radical Notation

Power Functions and Models

Equations Involving Rational Exponents

Equations Involving Radicals

Power Regression (Optional)

Checking Basic Concepts for Section 4.7

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Extended and Discovery Exercises

Chapters 1-4 Cumulative Review Exercises

Chapter 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS

5.1 Combining Functions

Arithmetic Operations on Functions

Composition of Functions

5.2 Inverse Functions and Their Representations

Inverse Operations

One-to-One Functions

Symbolic Representations of Inverse Functions

Other Representations of Inverse Functions

Checking Basic Concepts for Sections 5.1 and 5.2

5.3 Exponential Functions and Models

Linear and Exponential Growth

Exponential Models

Compound Interest

The Natural Exponential Function

5.4 Logarithmic Functions and Models

The Common Logarithmic Function

Basic Equations

Logarithms with Other Bases

General Logarithmic Equations

Checking Basic Concepts for Sections 5.3 and 5.4

5.5 Properties of Logarithms

Basic Properties of Logarithms

Change of Base Formula

5.6 Exponential and Logarithmic Equations

Exponential Equations

Logarithmic Equations

Checking Basic Concepts for 5.5 and 5.6

5.7 Constructing Nonlinear Models

Exponential Model

Logarithmic Model

Logistic Model

Checking Basic Concepts for Section 5.7

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Extended and Discovery Exercises

Chapter 6: TRIGONOMETRIC FUNCTIONS

6.1 Angles and Their Measure

Angles

Degree Measure

Radian Measure

Arc Length

Area of a Sector

6.2 Right Triangle Trigonometry

Basic Concepts of Trigonometric Functions

Applications of Right Triangle Trigonometry

Complementary Angles and Cofunctions

Checking Basic Concepts for 6.1 and 6.2

6.3 The Sine and Cosine Functions and Their Graphs

Definitions

The Unit Circle

Representations of the Sine and the Cosine Functions

Applications of the Sine and Cosine Functions

Modeling with the Sine Function (Optional)

6.4 Other Trigonometric Functions and Their Graphs

Definitions and Basic Identities

Representations of Other Trigonometric Functions

Applications of Trigonometric Functions

Checking Basic Concepts for Sections 6.3 and 6.4

6.5 Graphing Trigonometric Functions

Transformations of Trigonometric Graphs

Graphing Trigonometric Functions by Hand

Simple Harmonic Motion

Models Involving Trigonometric Functions (Optional)

6.6 Inverse Trigonometric Functions

Review of Inverses

The Inverse Sine Function

The Inverse Cosine Function

The Inverse Tangent Function

Solving Triangles and Equations

Checking Basic Concepts for Sections 6.5 and 6.6

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Extended and Discovery Exercises

Chapters 1-6 Cumulative Review Exercises

Chapter 7: TRIGONOMETRIC IDENTITIES AND EQUATIONS

7.1 Fundamental Identities

Reciprocal and Quotient Identities

Pythagorean Identities

Negative-Angle Identities

7.2 Verifying Identities

Simplifying Trigonometric Expressions

Verification of Identities

Checking Basic Concepts for Section 7.1 and 7.2

7.3 Trigonometric Equations

Reference Angles

Solving Trigonometric Equations

Solving Inverse Trigonometric Equations

7.4 Sum and Difference Identities

Sum and Difference Identities for Cosine

Other Sum and Difference Identities

Checking Basic Concepts for Section 7.3 and 7.4

7.5 Multiple-Angle Identities

Double-Angle Identities

Half-Angle Formulas

Solving Equations

Product-to-Sum and Sum-to-Product Identities

Checking Basic Concepts for Section 7.5

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Extended and Discovery Exercises

Chapter 8: FURTHER TOPICS IN TRIGONOMETRY

8.1 Law of Sines

Oblique Triangles

Solving Triangles

The Ambiguous Case

8.2 Law of Cosines

Derivation of the Law of Cosines

Solving Triangles

Area Formulas

Checking Basic Concepts for Sections 8.1 and 8.2

8.3 Vectors

Basic Concepts

Operations on Vectors

The Dot Product

Work

8.4 Parametric Equations

Basic Concepts

Applications of Parametric Equations

Checking Basic Concepts for Sections 8.3 and 8.4

8.5 Polar Equations

The Polar Coordinate System

Graphs of Polar Equations

Graphing Calculators and Polar Equations (Optional)

Solving Polar Equations

8.6 Trigonometric Form and Roots of Complex Numbers

Trigonometric Form

Products and Quotients of Complex Numbers

De Moivre's Theorem

Roots of Complex Numbers

Checking Basic Concepts for Sections 8.5 and 8.6

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Extended and Discovery Exercises

Chapters 1-8 Cumulative Review Exercises

Chapter 9: SYSTEMS OF EQUATIONS AND INEQUALITIES

9.1 Functions and Equations in Two Variables

Functions of Two Variables

Systems of Equations

The Method of Substitution

Graphical and Numerical Methods

Joint Variation

9.2 Systems of Equations and Inequalities in Two Variables

Types of Linear Systems in Two Variables

The Elimination Method

Systems of Linear and Nonlinear Inequalities

Linear Programming

Checking Basic Concepts for 9.1 and 9.2

9.3 Systems of Linear Equations in Three Variables

Basic Concepts

Solving with Elimination and Substitution

Systems with No Solutions

Systems with Infinitely Many Solutions

9.4 Solutions to Linear Systems Using Matrices

Representing Systems of Linear Equations with Matrices

Row-Echelon Form

Gaussian Elimination

Solving Systems of Linear Equations with Technology (Optional)

Checking Basic Concepts for Sections 9.3 and 9.4

9.5 Properties and Applications of Matrices

Matrix Notation

Sums, Differences, and Scalar Multiples of Matrices

Matrix Products

Technology and Matrices (Optional)

9.6 Inverses of Matrices

Matrix Inverses

Finding Inverses Symbolically

Representing Linear Systems with Matrix Equations

Solving Linear Systems with Inverses

Checking Basic Concepts for Sections 9.5 and 9.6

9.7 Determinants

Definition and Calculation of Determinants

Area of Regions

Cramer's Rule

Limitations on the Method of Cofactors and Cramer's Rule

Checking Basic Concepts for Section 9.7

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Extended and Discovery Exercise

Chapter 10: CONIC SECTIONS

10.1 Parabolas

Equations and Graphs of Parabolas

Reflective Property of Parabolas

Translations of Parabolas

10.2 Ellipses

Equations and Graphs of Ellipses

Reflective Property of Ellipses

Translations of Ellipses

Circles

Solving Systems of Equations and Inequalities

Checking Basic Concepts for Section 10.1 and 10.2

10.3 Hyperbolas

Equations and Graphs of Hyperbolas

Reflective Property of Hyperbolas

Translations of Hyperbolas

Solving Systems of Nonlinear Equations

Checking Basic Concepts for Section 10.3

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Extended and Discovery Exercises

Chapter 11: FURTHER TOPICS IN ALGEBRA

11.1 Sequences

Basic Concepts

Representations of Sequences

Arithmetic Sequences

Geometric Sequences

11.2 Series

Basic Concepts

Arithmetic Series

Geometric Series

Summation Notation

Checking Basic Concepts for Sections 11.1 and 11.2

11.3 Counting

Fundamental Counting Principle

Permutations

Combinations

11.4 The Binomial Theorem

Derivation of the Binomial Theorem

Pascal's Triangle

Checking Basic Concepts for Sections 11.3 and 11.4

11.5 Mathematical Induction

Mathematical Induction

Proving Statements

Generalized Principle of Mathematical Induction

11.6 Probability

Definition of Probability

Compound Events

Independent and Dependent Events

Checking Basic Concepts for Sections 11.5 and 11.6

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Extended and Discovery Exercises

Chapters 1-11 Cumulative Review Exercises

Chapter R: REFERENCE- BASIC CONCEPTS FROM ALGEBRA AND GEOMETRY

R.1 Formulas from Geometry

Geometric Shapes in a Plane

The Pythagorean Theorem

Three-Dimensional Objects

Similar Triangles

A Summary of Geometric Formulas

R.2 Circles

Equations and Graphs of Circles

Finding the Center and Radius of a Circle

R.3 Integer Exponents

Bases and Positive Exponents

Zero and Negative Exponents

Product, Quotient, and Power Rules

R.4 Polynomial Expressions

Addition and Subtraction of Monomials

Addition and Subtraction of Polynomials

Distributive Properties

Multiplying Polynomials

Some Special Products

R.5 Factoring Polynomials

Common Factors

Factoring by Grouping

Factoring x2 + bx + c

Factoring Trinomials by Grouping

Factoring Trinomials with FOIL

Difference of Two Squares

Perfect Square Trinomials

Sum and Difference of Two Cubes

R.6 Rational Expressions

Simplifying Rational Expressions

Multiplication and Division of Rational Expressions

Least Common Multiples

Common Denominators

Addition and Subtraction of Rational Expressions

Clearing Fractions

Complex Fractions

R.7 Radical Notation and Rational Exponents

Radical Notation

Rational Exponents

Properties of Rational Exponents

R.8 Radical Expressions

Product Rule for Radical Expressions

Quotient Rule for Radical Expressions

Addition and Subtraction

Multiplication

Rationalizing the Denominator

APPENDIX A: A Library of Functions

APPENDIX B: Using the Graphing Calculator

APPENDIX C: Partial Fractions

APPENDIX D: Rotation of Axes

Bibliography

Answers to Selected Exercises

Index of Applications

Index

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