Precalculus – Michael Sullivan – 11th Edition

1. Graphs
1.1 The Distance and Midpoint Formulas
1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
1.3 Lines
1.4 Circles
Chapter 1 Review, Test, and Projects

2. Functions and Their Graphs
2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions
Chapter 2 Review, Test, and Projects

3. Linear and Quadratic Functions
3.1 Properties of Linear Functions and Linear Models
3.2 Building Linear Models from Data
3.3 Quadratic Functions and Their Properties
3.4 Build Quadratic Models from Verbal Descriptions and from Data
3.5 Inequalities Involving Quadratic Functions
Chapter 3 Review, Test, and Projects

4. Polynomial and Rational Functions
4.1 Polynomial Functions
4.2 Graphing Polynomial Functions; Models
4.3 Properties of Rational Functions
4.4 The Graph of a Rational Function
4.5 Polynomial and Rational Inequalities
4.6 The Real Zeros of a Polynomial Function
Chapter 4 Review, Test, and Projects

5. Exponential and Logarithmic Functions
5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data
Chapter 5 Review, Test, and Projects

6. Trigonometric Functions
6.1 Angles, Arc, Length, and Circular Motion
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting
Chapter 6 Review, Test, and Projects

7. Analytic Trigonometry
7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions (Continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas
Chapter 7 Review, Test, and Projects

8. Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry; Applications
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
Chapter 8 Review, Test, and Projects

9. Polar Coordinates; Vectors
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; De Moivre’s Theorem
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Chapter 9 Review, Test, and Projects

10. Analytic Geometry
10.1 Conics
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
10.5 Rotation of Axes; General Form of a Conic
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Chapter 10 Review, Test, and Projects

11. Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination
11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition
11.6 Systems of Nonlinear Equations
11.7 Systems of Inequalities
11.8 Linear Programming
Chapter 11 Review, Test, and Projects

12. Sequences; Induction; the Binomial Theorem
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences; Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem
Chapter 12 Review, Test, and Projects

13. Counting and Probability
13.1 Counting
13.2 Permutations and Combinations
13.3 Probability
Chapter 13 Review, Test, and Projects

14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
14.1 Finding Limits Using Tables and Graphs
14.2 Algebra Techniques for Finding Limits
14.3 One-sided Limits; Continuous Functions
14.4 The Tangent Problem; The Derivative
14.5 The Area Problem; The Integral
Chapter 14 Review, Test, and Projects

Appendix A: Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Polynomials
A.4 Synthetic Division
A.5 Rational Expressions
A.6 Solving Equations
A.7 Complex Numbers; Quadratic Equations in the Complex Number System
A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
A.9 Interval Notation; Solving Inequalities
A.10 nth Roots; Rational Exponents

Appendix B: Graphing Utilities
B.1 The Viewing Rectangle
B.2 Using a Graphing Utility to Graph Equations
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
B.4 Using a Graphing Utility to Solve Equations
B.5 Square Screens
B.6 Using a Graphing Utility to Graph Inequalities
B.7 Using a Graphing Utility to Solve Systems of Linear Equations
B.8 Using a Graphing Utility to Graph a Polar Equation
B.9 Using a Graphing Utility to Graph Parametric
Equations