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Summary
The Barnett, Ziegler, Byleen, and Sobecki College Algebra series is designed to be user friendly and to maximize student comprehension by emphasizing computational skills, ideas, and problem solving as opposed to mathematical theory. Suitable for either one or two semester college algebra with trigonometry or precalculus courses, Precalculus introduces a unit circle approach to trigonometry and includes a chapter on limits to provide students with a solid foundation for calculus concepts. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A MathZone site featuring algorithmic exercises, videos, and other resources accompanies the text.
Table of Contents
Precalculus 7e
CHAPTER R: BASIC ALGEBRAIC OPERATIONS
R-1 Algebra and Real Numbers
R-2 Exponents and Radicals
R-3 Polynomials: Basic Operations and Factoring
R-4 Rational Expressions: Basic Operations
Chapter R Review
CHAPTER 1: EQUATIONS AND INEQUALITIES
1-1 Linear Equations and Applications
1-2 Linear Inequalities
1-3 Absolute Value
1-4 Complex Numbers
1-5 Quadratic Equations and Applications
1-6 Equations Involving Radicals
Chapter 1 Group Activity: Solving a Cubic Equation
Chapter 1 Review
CHAPTER 2: GRAPHS
2-1 Rectangular Coordinates
2-2 Distance in the Plane
2-3 Equations of a Line
2-4 Linear Equations and Models
Chapter 2 Group Activity: Rates of Change
Chapter 2 Review
CHAPTER 3: FUNCTIONS
3-1 Functions
3-2 Graphing Functions
3-3 Transformations of Functions
3-3 Quadratic Functions
3-5 Combining Functions; Composition
3-6 Inverse Functions
Chapter 3 Group Activity: Mathematical Modeling - Choosing a Long-Distance Calling Plan
Chapter 3 Review
1, 2, & 3 Cumulative Review Exercises
CHAPTER 4: POLYNOMIAL AND RATIONAL FUNCTIONS
4-1 Polynomial Functions And Models
4-2 Real Zeros and Polynomial Inequalities
4-3 Complex Zeros and Rational Zeros of Polynomials
4-4 Rational Functions and Inequalities
4-5 Variation and Modeling
Chapter 4 Group Activity: Interpolating Polynomials
Chapter 4 Review
CHAPTER 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
5-1 Exponential Functions
5-2 Exponential Models
5-3 Logarithmic Functions
5-4 Logarithmic Models
5-5 Exponential and Logarithmic Equations
Chapter 5 Group Activity: Growth of Increasing Functions
Chapter 5 Review
4 & 5 Cumulative Review Exercises
CHAPTER 6: TRIGONOMETRIC FUNCTIONS
6-1 Angles and Their Measure
6-2 Trigonometric Functions: A Unit Circle Approach
6-3 Solving Right Triangles
6-4 Trigonometric Functions: Properties and Graphs
6-5 More General Trigonometric Functions
6-6 Inverse Trigonometric Functions
Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer
Chapter 6 Review
CHAPTER 7: TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS
7-1 Basic Identities and Their Use
7-2 Sum, Difference, and Cofunction Identities
7-3 Double-Angle and Half-Angle Identities
7-4 Product-Sum and Sum-Product Identities
7-5 Trigonometric Equations
Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C) - A Harmonic Analysis Tool
Chapter 7 Review
CHAPTER 8: ADDITIONAL TOPICS IN TRIGONOMETRY
8-1 Law of Sines
8-2 Law of Cosines
8-3 Vectors in the Plane
8-4 Polar Coordinates and Graphs
8-5 Complex Numbers and De Moivre's Theorem
Chapter 8 Group Activity: Conic Sections and Planetary Orbits
Chapter 8 Review
6, 7, & 8 Cumulative Review Exercises
CHAPTER 9: ADDITIONAL TOPICS IN ANALYTIC GEOMETRY
9-1 Conic Sections; Parabola
9-2 Ellipse
9-3 Hyperbola
9-4 Rotation of Axes
Chapter 9 Group Activity: Focal Chords
Chapter 9 Review
CHAPTER 10: SYSTEMS OF EQUATIONS AND INEQUALITIES; MATRICES
10-1 Systems of Linear Equations
10-2 Solving Linear Systems Using Gauss-Jordan Elimination
10-3 Matrix Operations
10-4 Solving Linear Systems Using Inverse Matrices
10-5 Determinants and Cramer's Rule
Chapter 10 Group Activity: Modeling with Systems of Linear Equations
10-6 Systems of Nonlinear Equations
10-7 Systems of Linear Inequalities
10-8 Linear Programming
Chapter 10 Review
CHAPTER 11: SEQUENCES AND SERIES
11-1 Sequences and Series
11-2 Mathematical Induction
11-3 Arithmetic and Geometric Sequences
11-4 Counting Techniques: Multiplication Principle, Permutations, and Combinations
11-5 Sample Spaces and Probability
11-6 Binomial Formula
Chapter 11 Group Activity: Sequences Specified by Recursion Formulas
Chapter 11 Review
9. 10, & 11 Cumulative Review Exercises
CHAPTER 12: LIMITS: AN INTRODUCTION TO CALCULUS
12-1 Introduction to Limits
12-2 Computing Limits Algebraically
12-3 Limits at Infinity
12-4 The Derivative
12-5 Area and Calculus
Chapter 12 Group Activity: Derivatives of Exponential and Log Functions