Precalculus. Mathematics for Calculus

Cover
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Copyright
Contents
Preface
A Tribute to Lothar Redlin
To the Student
Technology in the Eighth Edition
Prologue: Principles of Problem Solving
Chapter 1: Fundamentals
	Chapter Overview
	1.1 Real Numbers
	1.2 Exponents and Radicals
	1.3 Algebraic Expressions
	1.4 Rational Expressions
	1.5 Equations
	1.6 Complex Numbers
	1.7 Modeling with Equations
	1.8 Inequalities
	1.9 The Coordinate Plane; Graphs of Equations; Circles
	1.10 Lines
	1.11 Solving Equations and Inequalities Graphically
	1.12 Modeling Variation
	Chapter 1 review
	Chapter 1 Test
	Focus on Modeling Fitting Lines to Data
Chapter 2: Functions
	Chapter Overview
	2.1 Functions
	2.2 Graphs of Functions
	2.3 Getting Information from the Graph of a Function
	2.4 Average Rate of Change of a Function
	2.5 Linear Functions and Models
	2.6 Transformations of Functions
	2.7 Combining Functions
	2.8 One-to-One Functions and Their Inverses
	chapter 2 Review
	Chapter 2 Test
	Focus on Modeling Modeling with Functions
Chapter 3: Polynomial and Rational Functions
	Chapter Overview
	3.1 Quadratic Functions and Models
	3.2 Polynomial Functions and Their Graphs
	3.3 Dividing Polynomials
	3.4 Real Zeros of Polynomials
	3.5 Complex Zeros and the Fundamental Theorem of Algebra
	3.6 Rational Functions
	3.7 Polynomial and Rational Inequalities
	Chapter 3 review
	Chapter 3 Test
	Focus on Modeling Fitting Polynomial Curves to Data
Chapter 4: Exponential and Logarithmic Functions
	4.1 Exponential Functions
	4.2 The Natural Exponential Function
	4.3 Logarithmic Functions
	4.4 Laws of Logarithms
	4.5 Exponential and Logarithmic Equations
	4.6 Modeling with Exponential Functions
	4.7 Logarithmic Scales
	Chapter 4 Review
	Chapter 4 Test
	Focus on Modeling Fitting Exponential and Power Curves to Data
	Cumulative Review Test: Chapters 2, 3, and 4 (Website)
Chapter 5: Trigonometric Functions: Unit Circle Approach
	Chapter Overview
	5.1 The Unit Circle
	5.2 Trigonometric Functions of Real Numbers
	5.3 Trigonometric Graphs
	5.4 More Trigonometric Graphs
	5.5 Inverse Trigonometric Functions and Their Graphs
	5.6 Modeling Harmonic Motion
	Chapter 5 Review
	Chapter 5 Test
	Focus on Modeling Fitting Sinusoidal Curves to Data
Chapter 6: Trigonometric Functions: Right Triangle Approach
	6.1 Angle Measure
	6.2 Trigonometry of Right Triangles
	6.3 Trigonometric Functions of Angles
	6.4 Inverse Trigonometric Functions and Right Triangles
	6.5 The Law of Sines
	6.6 The Law of Cosines
	chapter 6 review
	Chapter 6 Test
	Focus on Modeling Surveying
Chapter 7: Analytic Trigonometry
	Chapter Overview
	7.1 Trigonometric Identities
	7.2 Addition and Subtraction Formulas
	7.3 Double-Angle, Half-Angle, and Product-Sum Formulas
	7.4 Basic Trigonometric Equations
	7.5 More Trigonometric Equations
	Chapter 7 Review
	Chapter 7 Test
	Focus on Modeling Traveling and Standing Waves
	Cumulative Review Test: Chapters 5, 6, and 7 (Website)
Chapter 8: Polar Coordinates, Parametric Equations, and Vectors
	Chapter Overview
	8.1 Polar Coordinates
	8.2 Graphs of Polar Equations
	8.3 Polar Form of Complex Numbers; De Moivre’s Theorem
	8.4 Plane Curves and Parametric Equations
	8.5 Vectors
	8.6 The Dot Product
	Chapter 8 review
	Chapter 8 Test
	Focus on Modeling The Path of a Projectile
Chapter 9: Systems of Equations and Inequalities
	Chapter Overview
	9.1 Systems of Linear Equations in Two Variables
	9.2 Systems of Linear Equations in Several Variables
	9.3 Matrices and Systems of Linear Equations
	9.4 The Algebra of Matrices
	9.5 Inverses of Matrices and Matrix Equations
	9.6 Determinants and Cramer’s Rule
	9.7 Partial Fractions
	9.8 Systems of Nonlinear Equations
	9.9 Systems of Inequalities
	Chapter 9 Review
	Chapter 9 Test
	Focus on Modeling Linear Programming
Chapter 10: Conic Sections
	Chapter Overview
	10.1 Parabolas
	10.2 Ellipses
	10.3 Hyperbolas
	10.4 Shifted Conics
	10.5 Rotation of Axes
	10.6 Polar Equations of Conics
	chapter 10 review
	Chapter 10 Test
	Focus on Modeling Conics in Architecture
	Cumulative Review Test: Chapters 8, 9, and 10 (Website)
Chapter 11: Sequences and Series
	Chapter Overview
	11.1 Sequences and Summation Notation
	11.2 Arithmetic Sequences
	11.3 Geometric Sequences
	11.4 Mathematical Induction
	11.5 The Binomial Theorem
	chapter 11 review
	Chapter 11 Test
	Focus on Modeling Modeling with Recursive Sequences
Chapter 12: Limits: A Preview of Calculus
	Chapter Overview
	12.1 Finding Limits Numerically and Graphically
	12.2 Finding Limits Algebraically
	12.3 Tangent Lines and Derivatives
	12.4 Limits at Infinity; Limits of Sequences
	12.5 Areas
	chapter 12 review
	Chapter 12 Test
	Focus on Modeling Interpretations of Area
	Cumulative Review Test: Chapters 11 and 12 (Website)
Appendix A: Geometry Review
APPENDIX B: Calculations and Significant Figures (Website)
APPENDIX C: Graphing with a Graphing Calculator (Website)
APPENDIX D: Using the TI-83/84 Graphing Calculator (Website)
APPENDIX E: Three-Dimensional Coordinate Geometry (Website)
APPENDIX F: Mathematics of Finance (Website)
APPENDIX G: Probability and Statistics (Website)
Answers
Index