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Precalculus with Modeling and Visualization

ISBN: 9780321279071 | 0321279077
Edition: 3rd
Format: Hardcover
Publisher: Addison Wesley
Pub. Date: 1/1/2006

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SummaryTable of Contents
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.
Prefacexv
Introduction to Functions and Graphs
1(71)
Numbers, Data, and Problem Solving
2(12)
... MORE
Sets of Numbers
Scientific Notation
Problem Solving
Visualization of Data
14(15)
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
29(1)
Functions and Their Representations
29(17)
Basic Concepts
Representations of Functions
Formal Definition of a Function
Graphing Calculators and Functions (Optional)
Identifying Functions
Types of Functions and Their Rates of Change
46(26)
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
62(1)
Chapter 1 Summary
62(4)
Chapter 2 Review Exercises
66(4)
Chapter 3 Extended and Discovery Exercises
70(2)
Linear Functions and Equations
72(99)
Linear Functions and Models
73(14)
Exact and Approximate Models
Representations of Linear Functions
Modeling with Linear Functions
Linear Regression (Optional)
Equations of Lines
87(19)
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
106(1)
Linear Equations
106(17)
Equations
Symbolic Solutions
Graphical and Numerical Solutions
Problem-Solving Strategies
Linear Inequalities
123(17)
Inequalities
Interval Notation
Techniques for Solving Inequalities
Compound Inequalities
Checking Basic Concepts for Sections 2.3 and 2.4
139(1)
Piecewise-Defined Functions
140(31)
Evaluating and Graphing Piecewise-Defined Functions
The Greatest Integer Function
The Absolute Value Function
Equations and Inequalities Involving Absolute Values
Checking Basic Concepts for Sections 2.5
158(1)
Chapter 2 Summary
158(4)
Chapter 2 Review Exercises
162(4)
Chapter 2 Extended and Discovery Exercises
166(1)
Chapter 1--2 Cumulative Review Exercises
167(4)
Quadratic Functions and Equations
171(70)
Quadratic Functions and Models
172(17)
Basic Concepts
Completing the Square and the Vertex Formula
Applications and Models
Quadratic Regression (Optional)
Quadratic Equations and Problem Solving
189(17)
Basic Concepts
Solving Quadratic Equations
Problem Solving
Checking Basic Concepts for Sections 3.1 and 3.2
205(1)
Quadratic Inequalities
206(10)
Graphical Solutions
Symbolic Solutions
Transformations of Graphs
216(25)
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
233(1)
Chapter 3 Summary
234(3)
Chapter 3 Review Exercises
237(2)
Chapter 3 Extended and Discovery Exercises
239(2)
Nonlinear Functions and Equations
241(122)
Nonlinear Functions and Their Graphs
242(15)
Polynomial Functions
Increasing and Decreasing Functions
Extrema of Nonlinear Functions
Symmetry
Polynomial Functions and Models
257(17)
Graphs of Polynomial Functions
Piecewise-Defined Polynomial Functions
Polynomial Regression (Optional)
Checking Basic Concepts for Sections 4.1 and 4.2
273(1)
Real Zeros of Polynomial Functions
274(19)
Division of Polynomials
Factoring Polynomials
Graphs and Multiple Zeros
Rational Zeros
Polynomial Equations
The Fundamental Theorem of Algebra
293(12)
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
305(1)
Rational Functions and Models
305(20)
Rational Functions
Vertical Asymptotes
Horizontal Asymptotes
Identifying Asymptotes
Rational Equations
Variation
Polynomial and Rational Inequalities
325(9)
Polynomial Inequalities
Rational Inequalities
Checking Basic Concepts for Sections 4.5 and 4.6
334(1)
Power Functions and Radical Equations
334(29)
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
346(1)
Chapter 4 Summary
347(5)
Chapter 4 Review Exercises
352(5)
Chapter 4 Extended and Discovery Exercises
357(1)
Chapters 1--4 Cumulative Review Exercises
358(5)
Exponential and Logarithmic Functions
363(111)
Combining Functions
364(18)
Arithmetic Operations on Functions
Composition of Functions
Inverse Functions and Their Representations
382(17)
Inverse Operations
One-to-One Functions
Symbolic Representation of Inverse Functions
Other Representations of Inverse Functions
Checking Basic Concepts for Sections 5.1 and 5.2
399(1)
Exponential Functions and Models
399(20)
Linear and Exponential Growth
Exponential Models
Compound interest
The Natural Exponential Function
Logarithmic Functions and Models
419(17)
The Common Logarithmic Function
Basic Equations
Logarithms with Other Bases
General Logarithmic Equations
Checking Basic Concepts for Sections 5.3 and 5.4
435(1)
Properties of Logarithms
436(8)
Basic Properties of Logarithms
Change of Base Formula
Exponential and Logarithmic Equations
444(13)
Exponential Equations
Logarithmic Equations
Checking Basic Concepts for Sections 5.5 and 5.6
457(1)
Constructing Nonlinear Models
457(17)
Exponential Model
Logarithmic Model
Logistic Model
Checking Basic Concepts for Section 5.7
464(1)
Chapter 5 Summary
464(4)
Chapter 5 Review Exercises
468(4)
Extended and Discovery Exercises
472(2)
Trigonometric Functions
474(107)
Angles and Their Measures
475(15)
Angles
Degree Measure
Radian Measure
Arc Length
Area of Sector
Right Triangle Trigonometry
490(14)
Basic Concepts of Trigonometric Functions
Applications of Right Triangle Trigonometry
Complementary Angles and Confunctions
Checking Basic Concepts for Sections 6.1 and 6.2
503(1)
The Sine and Cosine Functions and Their Graphs
504(14)
Definitions
The Unite Circle
Representations of the Sine and Cosine Functions
Applications of the Sine and Cosine Functions
Modeling with the Sine Function (Optional)
Other Trigonometric Functions and Their Graphs
518(14)
Definitions and Basic Identities
Representations of Other Trigonometric Functions
Applications of Trigonometric Functions
Checking Basic Concepts for Sections 6.3 and 6.4
531(1)
Graphing Trigonometric Functions
532(18)
Transformations of Trigonometric Graphs
Graphing Trigonometric Functions by Hand
Simple Harmonic Motion
Models Involving Trigonometric Functions (Optional)
Inverse Trigonometric Functions
550(31)
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
566(1)
Chapter 6 Summary
567(3)
Chapter 6 Review Exercises
570(3)
Extended and Discovery Exercises
573(2)
Chapters 1--6 Cumulative Review Exercises
575(6)
Trigonometric Identities and Equations
581(71)
Fundamental Identities
582(12)
Reciprocal and Quotient Identities
Pythagorean Identities
Negative-Angle Identities
Verifying Identities
594(8)
Simplifying Trigonometric Expressions
Verification of Identities
Checking Basic Concepts for Sections 7.1 and 7.2
601(1)
Trigonometric Equations
602(14)
Reference Angles
Solving Trigonometric Equations
Solving Inverse
Trigonometric Equations
Sum and Difference Identities
616(12)
Sum and Difference Identities for Cosine
Other Sum and Difference Identities
Derivation of an Identity
Checking Basic Concepts for Sections 7.3 and 7.4
628(1)
Multiple-Angle Identities
628(24)
Double-Angle Identities
Half-Angle Formulas
Solving Equations
Product-to-Sum and Sum-to-Product Identities
Checking Basic Concepts for Section 7.5
644(1)
Chapter 7 Summary
645(3)
Chapter 7 Review Exercises
648(2)
Extended and Discovery Exercises
650(2)
Further Topics in Trigonometry
652(86)
Law of Sines
653(11)
Oblique Triangles
Solving Triangles
The Ambiguous Case
Law of Cosines
664(12)
Derivation of the Law of Cosines
Solving Triangles
Area Formulas
Checking Basic Concepts for Sections 8.1 and 8.2
675(1)
Vectors
676(15)
Basic Concepts
Operations on Vectors
The Dot Product
Work
Parametric Equations
691(11)
Basic Concepts
Applications of Parametric Equations
Checking Basic Concepts for Sections 8.3 and 8.4
701(1)
Polar Equations
702(12)
The Polar Coordinate System
Graphs of Polar Equations
Graphing Calculators and Polar Equations (Optional)
Solving Polar Equations
Trigonometric Form and Roots of Complex Numbers
714(24)
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
725(1)
Chapter 8 Summary
726(3)
Chapter 8 Review and Exercises
729(2)
Extended and Discovery Exercises
731(2)
Chapters 1--8 Cumulative Review Exercises
733(5)
Systems of Equations and Inequalities
738(106)
Functions and Equations in Two Variables
739(15)
Functions of Two Variables
Systems of Equations
The Method of Substitution
Graphical and Numerical Methods
Joint Variation
Systems of Equations and Inequalities in Two Variables
754(18)
Types of Linear Systems in Two Variables
The Elimination Method
Systems of Linear and Nonlinear Inequalities
Linear Programming
Checking Basic Concepts for Sections 9.1 and 9.2
772(1)
Systems of Linear Equations in Three Variables
772(8)
Basic Concepts
Solving with Elimination and Substitution
Systems with No Solutions
Systems with Infinitely Many Solutions
Solutions to Linear Systems Using Matrices
780(17)
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
796(1)
Properties and Applications of Matrices
797(14)
Matrix Notation
Sums, Differences, and Scalar Multipies of Matrices
Matrix Products
Technology and Matrices (Optional)
Inverses of Matrices
811(14)
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
824(1)
Determinants
825(19)
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
833(1)
Chapter 9 Summary
834(4)
Chapter 9 Review Exercises
838(3)
Extended and Discovery Exercises
841(3)
Conic Sections
844(43)
Parabolas
845(10)
Equations and Graphs of Parabolas
Reflective Property of Parabolas
Translations of Parabolas
Ellipses
855(15)
Equations and Graphs of Ellipses
Reflective Property of Ellipses
Translations of Ellipses
Circles
Solving Systems of Nonlinear Equations and Inequalities
Checking Basic Concepts for Sections 10.1 and 10.2
870(1)
Hyperbolas
870(17)
Equations and Graphs of Hyperbolas
Reflective Property of Hyperbolas
Translations of Hyperbolas
Solving Systems of Nonlinear Equations
Checking Basic Concepts for Section 10.3
881(1)
Chapter 10 Summary
882(2)
Chapter 10 Review Exercises
884(2)
Extended and Discovery Exercises
886(1)
Further Topics in Algebra
887
Sequences
888(14)
Basic Concepts
Representations of Sequences
Arithmetic Sequences
Geometric Sequences
Series
902(16)
Basic Concepts
Arthmetic Series
Geometric Series
Summation Notation
Checking Basic Concepts for Sections 11.1 and 11.2
918(1)
Counting
918(11)
Fundamental Counting Principle
Permutations
Combinations
The Binomial Theorem
929(6)
Derivation of the Binomial Theorem
Pascal's Triangle
Checking Basic Concepts for Sections 11.3 and 11.4
934(1)
Mathematical Induction
935(6)
Mathematical Induction
Proving Statements
Generalized Principle of Mathematical Induction
Probability
941
Definition of Probability
Compound Events
Independent and Dependent Events
Checking Basic Concepts for Sections 11.5 and 11.6
954(1)
Chapter 11 Summary
954(4)
Chapter 11 Review Exercises
958(2)
Extended and Discovery Exercises
960(1)
Chapters 1--1 Cumulative Review Exercises
961
Reference: Basic Concepts from Algebra and Geometry
1(1)
Formulas from Geometry
1(9)
Geometric Shapes in a Plane
The Pythagorean Theorem
Three-Dimensional Objects
Similar Triangles
A Summary of Geometric Formulas
Circles
10(3)
Equations and Graphs of Circles
Finding the Center and Radius of a Circle
Integer Exponents
13(7)
Bases and Positive Exponents
Zero and Negative Exponents
Product, Quotient, and Power Rules
Polynomial Expressions
20(7)
Addition and Subtraction of Monomials
Addition and Subtraction of Polynomials
Distributive Properties
Multiplying Polynomials
Some Special Products
Factoring Polynomials
27(11)
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
Rational Expressions
38(10)
Simplifying Rational Expressions
Multiplication and Division of Rational Expressions
Least Common Multiples
Common Denominators
Addition and Subtraction of Rational Expressions
Clearing Fractions
Complex Fractions
Radical Notation and Rational Exponents
48(7)
Radical Notation
Rational Exponents
Properties of Rational Exponents
Radical Expressions
55
Product Rule for Radical Expressions
Quotient Rule for Radical Expressions
Addition and Subtraction
Multiplication
Rationalizing the Denominator
Appendix A: A Library of Functions1(4)
Appendix B: Using the Graphing Calculator5(23)
Appendix C: Partial Fractions28(6)
Appendix D: Rotation of Axes34
Bibliography1(1)
Answers to Selected Exercises1(1)
Index of Applications1(6)
Index7

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