Table of Contents

CHAPTER P - PREREQUISITES

  • P.1 Real Numbers
  • P.2 Cartesian Coordinate System
  • P.3 Linear Equations and Inequalities
  • P.4 Lines in the Plane
  • P.5 Solving Equations Graphically, Numerically, and Algebraically
  • P.6 Complex Numbers
  • P.7 Solving Inequalities Algebraically and Graphically

CHAPTER 1 - FUNCTIONS AND GRAPHS

  • 1.1 Modeling and Equation Solving
  • 1.2 Functions and Their Properties
  • 1.3 Twelve Basic Functions
  • 1.4 Building Functions from Functions
  • 1.5 Parametric Relations and Inverses
  • 1.6 Graphical Transformations
  • 1.7 Modeling with Functions

CHAPTER 2 - POLYNOMIAL, POWER, AND RATIONAL FUNCTIONS

  • 2.1 Linear and Quadratic Functions and Modeling
  • 2.2 Modeling with Power Functions
  • 2.3 Polynomial Functions of Higher Degree with Modeling
  • 2.4 Real Zeros of Polynomial Functions
  • 2.5 Complex Zeros and the Fundamental Theorem of Algebra
  • 2.6 Graphs of Rational Functions
  • 2.7 Solving Equations in One Variable
  • 2.8 Solving Inequalities in One Variable

CHAPTER 3 - EXPONENTIAL, LOGISTIC, AND LOGARITHMIC FUNCTIONS

  • 3.1 Exponential and Logistic Functions
  • 3.2 Exponential and Logistic Modeling
  • 3.3 Logarithmic Functions and Their Graphs
  • 3.4 Properties of Logarithmic Functions
  • 3.5 Equation Solving and Modeling
  • 3.6 Mathematics of Finance

CHAPTER 4 - TRIGONOMETRIC FUNCTIONS

  • 4.1 Angles and Their Measures
  • 4.2 Trigonometric Functions of Acute Angles
  • 4.3 Trigonometry Extended: The Circular Functions
  • 4.4 Graphs of Sine and Cosine: Sinusoids
  • 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant
  • 4.6 Graphs of Composite Trigonometric Functions
  • 4.7 Inverse Trigonometric Functions
  • 4.8 Solving Problems with Trigonometry

CHAPTER 5 - ANALYTIC TRIGONOMETRY

  • 5.1 Fundamental Identities
  • 5.2 Proving Trigonometric Identities
  • 5.3 Sum and Difference Identities
  • 5.4 Multiple-Angle Identities
  • 5.5 The Law of Sines
  • 5.6 The Law of Cosines

CHAPTER 6 - APPLICATIONS OF TRIGONOMETRY

  • 6.1 Vectors in the Plane
  • 6.2 Dot Product of Vectors
  • 6.3 Parametric Equations and Motion
  • 6.4 Polar Coordinates
  • 6.5 Graphs of Polar Equations
  • 6.6 De Moivre’s Theorem and nth Roots

CHAPTER 7 - SYSTEMS AND MATRICES

  • 7.1 Solving Systems of Two Equations
  • 7.2 Matrix Algebra
  • 7.3 Multivariate Linear Systems and Row Operations
  • 7.4 Systems of Inequalities in Two Variables

CHAPTER 8 - ANALYTIC GEOMETRY IN TWO AND THREE DIMENSIONS

  • 8.1 Conic Sections and a New Look at Parabolas
  • 8.2 Circles and Ellipses
  • 8.3 Hyperbolas
  • 8.4 Quadratic Equations with xy Terms 8.5 Polar Equations of Conics 8.6 Three-Dimensional Cartesian Coordinate System

CHAPTER 9 - DISCRETE MATHEMATICS

  • 9.1 Basic Combinatorics
  • 9.2 Binomial Theorem
  • 9.3 Sequences
  • 9.4 Series
  • 9.5 Mathematical Induction

CHAPTER 10 - STATISTICS AND PROBABILITY

  • 10.1 Probability
  • 10.2 Statistics (Graphical)
  • 10.3 Statistics (Numerical)
  • 10.4 Random Variables and Probability Models
  • 10.5 Statistical Literacy

CHAPTER 11 - AN INTRODUCTION TO CALCULUS: LIMITS, DERIVATIVES, AND INTEGRALS

  • 11.1 Limits and Motion: The Tangent Problem
  • 11.2 Limits and Motion: The Area Problem
  • 11.3 More on Limits
  • 11.4 24 Numerical Derivatives and Integrals

APPENDIX A - ALGEBRA REVIEW

  • A.1 Radicals and Rational Exponents
  • A.2 Polynomials and Factoring
  • A.3 Fractional Expressions

APPENDIX B – LOGIC

  • B.1 Logic: An Introduction
  • B.2 Conditionals and Biconditionals

APPENDIX C - KEY FORMULAS

  • C.1 Formulas from Algebra
  • C.2 Formulas from Geometry
  • C.3 Formulas from Trigonometry
  • C.4 Formulas from Analytic Geometry
  • C.5 Gallery of Basic Functions Bibliography Glossary Additional Answers Applications Index Index