Table of Contents

P. Prerequisites: Fundamental Concepts of Algebra

  • P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
  • P.2 Exponents and Scientific Notation
  • P.3 Radicals and Rational Exponents
  • P.4 Polynomials
  • P.5 Factoring Polynomials
  • P.6 Rational Expressions

1. Functions and Graphs

  • 1.1 Graphs and Graphing Utilities
  • 1.2 Basics of Functions and Their Graphs
  • 1.3 More on Functions and Their Graphs
  • 1.4 Linear Functions and Slope
  • 1.5 More on Slope
  • 1.6 Transformations of Functions
  • 1.7 Combinations of Functions; Composite Functions
  • 1.8 Inverse Functions
  • 1.9 Distance and Midpoint Formulas; Circles 

2. Polynomial and Rational Functions

  • 2.1 Complex Numbers
  • 2.2 Quadratic Functions
  • 2.3 Polynomial Functions and Their Graphs
  • 2.4 Dividing Polynomials; Remainder and Factor Theorems
  • 2.5 Zeros of Polynomial Functions
  • 2.6 Rational Functions and Their Graphs
  • 2.7 Polynomial and Rational Inequalities
  • 2.8 Modeling Using Variation

3. Exponential and Logarithmic Functions

  • 3.1 Exponential Functions
  • 3.2 Logarithmic Functions
  • 3.3 Properties of Logarithms
  • 3.4 Exponential and Logarithmic Equations
  • 3.5 Exponential Growth and Decay; Modeling Data

4. Trigonometric Functions

  • 4.1 Angles and Radian 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 of Trigonometric Functions 

5. Analytic Trigonometry

  • 5.1 Verifying Trigonometric Identities
  • 5.2 Sum and Difference Formulas
  • 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
  • 5.4 Product-to-Sum and Sum-to-Product Formulas
  • 5.5 Trigonometric Equations

6. Additional Topics in Trigonometry

  • 6.1 The Law of Sines
  • 6.2 The Law of Cosines
  • 6.3 Polar Coordinates
  • 6.4 Graphs of Polar Equations
  • 6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
  • 6.6 Vectors
  • 6.7 The Dot Product

7. Systems of Equations and Inequalities

  • 7.1 Systems of Linear Equations in Two Variables
  • 7.2 Systems of Linear Equations in Three Variables
  • 7.3 Partial Fractions
  • 7.4 Systems of Nonlinear Equations in Two Variables
  • 7.5 Systems of Inequalities
  • 7.6 Linear Programming

8. Matrices and Determinants

  • 8.1 Matrix Solutions to Linear Systems
  • 8.2 Inconsistent and Dependent Systems and Their Applications
  • 8.3 Matrix Operations and Their Applications
  • 8.4 Multiplicative Inverses of Matrices and Matrix Equations
  • 8.5 Determinants and Cramer's Rule

9. Conic Sections and Analytic Geometry

  • 9.1 The Ellipse
  • 9.2 The Hyperbola
  • 9.3 The Parabola
  • 9.4 Rotation of Axes
  • 9.5 Parametric Equations
  • 9.6 Conic Sections in Polar Coordinates 

10. Sequences, Induction, and Probability

  • 10.1 Sequences and Summation Notation
  • 10.2 Arithmetic Sequences
  • 10.3 Geometric Sequences and Series
  • 10.4 Mathematical Induction
  • 10.5 The Binomial Theorem
  • 10.6 Counting Principles, Permutations, and Combinations
  • 10.7 Probability

11. Introduction to Calculus

  • 11.1 Finding Limits Using Tables and Graphs
  • 11.2 Finding Limits Using Properties of Limits
  • 11.3 Limits and Continuity
  • 11.4 Introduction to Derivatives