Precalculus by Ron Larson, Robert P. Hostetler, Robert Hostetler

Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving.

• 1. Functions and Their Graphs
  1.1 Rectangular Coordinates
  1.2 Graphs of Equations
  1.3 Linear Equations in Two Variables
  1.4 Functions
  1.5 Analyzing Graphs of Functions
  1.6 A Library of Parent Functions
  1.7 Transformations of Functions
  1.8 Combinations of Functions: Composite Functions
  1.9 Inverse Functions
  1.10 Mathematical Modeling and Variation

  2. Polynomial and Rational Functions

  2.1 Quadratic Functions and Models

  2.2 Polynomial Functions of Higher Degree

  2.3 Polynomial and Synthetic Division

  2.4 Complex Numbers

  2.5 Zeros of Polynomial Functions

  2.6 Rational Functions

  2.7 Nonlinear Inequalities

  3. Exponential and Logarithmic Functions

  3.1 Exponential Functions and Their Graphs

  3.2 Logarithmic Functions and Their Graphs

  3.3 Properties of Logarithms

  3.4 Exponential and Logarithmic Equations

  3.5 Exponential and Logarithmic Models

  Cumulative Test: Chapters 1–3

  4. Trigonometry

  4.1 Radian and Degree Measure

  4.2 Trigonometric Functions: The Unit Circle

  4.3 Right Triangle Trigonometry

  4.4 Trigonometric Functions of Any Angle

  4.5 Graphs of Sine and Cosine Functions

  4.6 Graphs of Other Trigonometric Functions

  4.7 Inverse Trigonometric Functions

  4.8 Applications and Models

  5. Analytic Trigonometry

  5.1 Using Fundamental Identities

  5.2 Verifying Trigonometric Identities

  5.3 Solving Trigonometric Equations

  5.4 Sum and Difference Formulas

  5.5 Multiple–Angleand Product–to–Sum Formulas

  6. Additional Topics in Trigonometry

  6.1 Law of Sines

  6.2 Law of Cosines

  6.3 Vectors in the Plane

  6.4 Vectors and Dot Products

  6.5 Trigonometric Form of a Complex Number

  Cumulative Test: Chapters 4–6

  7. Systems of Equations and Inequalities

  7.1 Linear and Nonlinear Systems of Equations

  7.2 Two–Variable Linear Systems

  7.3 Multivariable Linear Systems

  7.4 Partial Fractions

  7.5 Systems of Inequalities

  7.6 Linear Programming

  8. Matrices and Determinants

  8.1 Matrices and Systems of Equations

  8.2 Operations with Matrices

  8.3 The Inverse of a Square Matrix

  8.4 The Determinant of a Square Matrix

  8.5 Applications of Matrices and Determinants

  9. Sequences, Series, and Probability

  9.1 Sequences and Series

  9.2 Arithmetic Sequences and Partial Sums

  9.3 Geometric Sequences and Series

  9.4 Mathematical Induction

  9.5 The Binomial Theorem

  9.6 Counting Principles

  9.7 Probability

  Cumulative Test: Chapters 7–9

  10. Topics in Analytic Geometry

  10.1 Lines

  10.2 Introduction to Conics: Parabolas

  10.3 Ellipses

  10.4 Hyperbolas

  10.5 Rotation of Conics

  10.6 Parametric Equations

  10.7 Polar Coordinates

  10.8 Graphs of Polar Equations

  10.9 Polar Equations of Conics

  Appendix A. Review of Fundamental Concepts of Algebra

  A.1 Real Numbers and Their Properties

  A.2 Exponents and Radicals

  A.3 Polynomials and Factoring

  A.4 Rational Expressions

  A.5 Solving Equations

  A.6 Linear Inequalities in One Variable

  A.7 Errors and the Algebra of Calculus

  Appendix B. Concepts in Statistics (web)

  B.1 Representing Data

  B.2 Measures of Central Tendency and Dispersion

  B.3 Least Squares Regression