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. Equations and Inequalities

  • 1.1 Graphs and Graphing Utilities
  • 1.2 Linear Equations and Rational Equations
  • 1.3 Models and Applications
  • 1.4 Complex Numbers
  • 1.5 Quadratic Equations
  • 1.6 Other Types of Equations
  • 1.7 Linear Inequalities and Absolute Value Inequalities 

2. Functions and Graphs

  • 2.1 Basics of Functions and Their Graphs
  • 2.2 More on Functions and Their Graphs
  • 2.3 Linear Functions and Slope
  • 2.4 More on Slope
  • 2.5 Transformations of Functions
  • 2.6 Combinations of Functions; Composite Functions
  • 2.7 Inverse Functions
  • 2.8 Distance and Midpoint Formulas; Circles 

3. Polynomial and Rational Functions

  • 3.1 Quadratic Functions
  • 3.2 Polynomial Functions and Their Graphs
  • 3.3 Dividing Polynomials; Remainder and Factor Theorems
  • 3.4 Zeros of Polynomial Functions
  • 3.5 Rational Functions and Their Graphs
  • 3.6 Polynomial and Rational Inequalities
  • 3.7 Modeling Using Variation 

4. Exponential and Logarithmic Functions

  • 4.1 Exponential Functions
  • 4.2 Logarithmic Functions
  • 4.3 Properties of Logarithms
  • 4.4 Exponential and Logarithmic Equations
  • 4.5 Exponential Growth and Decay; Modeling Data

5. Trigonometric Functions

  • 5.1 Angles and Radian Measure
  • 5.2 Right Triangle Trigonometry
  • 5.3 Trigonometric Functions of Any Angle
  • 5.4 Trigonometric Functions of Real Numbers; Periodic Functions
  • 5.5 Graphs of Sine and Cosine Functions
  • 5.6 Graphs of Other Trigonometric Functions
  • 5.7 Inverse Trigonometric Functions
  • 5.8 Applications of Trigonometric Functions

6. Analytic Trigonometry

  • 6.1 Verifying Trigonometric Identities
  • 6.2 Sum and Difference Formulas
  • 6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
  • 6.4 Product-to-Sum and Sum-to-Product Formulas
  • 6.5 Trigonometric Equations

7. Additional Topics in Trigonometry

  • 7.1 The Law of Sines
  • 7.2 The Law of Cosines
  • 7.3 Polar Coordinates
  • 7.4 Graphs of Polar Equations
  • 7.5 Complex Numbers in Polar Form; DeMoivre's Theorem
  • 7.6 Vectors
  • 7.7 The Dot Product

8. Systems of Equations and Inequalities

  • 8.1 Systems of Linear Equations in Two Variables
  • 8.2 Systems of Linear Equations in Three Variables
  • 8.3 Partial Fractions
  • 8.4 Systems of Nonlinear Equations in Two Variables
  • 8.5 Systems of Inequalities
  • 8.6 Linear Programming

9. Matrices and Determinants

  • 9.1 Matrix Solutions to Linear Systems
  • 9.2 Inconsistent and Dependent Systems and Their Applications
  • 9.3 Matrix Operations and Their Applications
  • 9.4 Multiplicative Inverses of Matrices and Matrix Equations
  • 9.5 Determinants and Cramer's Rule

10. Conic Sections and Analytic Geometry

  • 10.1 The Ellipse
  • 10.2 The Hyperbola
  • 10.3 The Parabola
  • 10.4 Rotation of Axes
  • 10.5 Parametric Equations
  • 10.6 Conic Sections in Polar Coordinates

11. Sequences, Induction, and Probability

  • 11.1 Sequences and Summation Notation
  • 11.2 Arithmetic Sequences
  • 11.3 Geometric Sequences and Series
  • 11.4 Mathematical Induction
  • 11.5 The Binomial Theorem
  • 11.6 Counting Principles, Permutations, and Combinations
  • 11.7 Probability