Precalculus Book

Chapter 1: Equations and Inequalities

1-1 Linear Equations, Formulas, and Problem Solving

1-2 Linear Inequalities in One Variable

1-3 Absolute Value Equations and Inequalities

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

Chapter 2: Relations, Functions and Graphs

2-1 Rectangular Coordinates; Graphing Circles and Relations

2-2 Graphs of Linear Equations

2-3 Linear Equations and Rates of Change

2-4 Functions, Notation, and Graphs of Functions

2-5 Analyzing the Graph of a Function

2-6 Toolbox Functions and Transformations

2-7 Piecewise-Defined Functions

2-8 The Algebra and Composition of Functions

Chapter 3: Polynomial and Rational Functions

3-1 Quadratic Functions and Applications

3-2 Synthetic Division; The Remainder and Factor Theorems

3-3 The Zeroes of Polynomial Functions

3-4 Graphing Polynomial Functions

3-5 Graphing Rational Functions

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential Functions

4-3 Logarithms and Logarithmic Functions

4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

4-5 Applications from Business, Finance, and Science

Chapter 5: Introduction to Trigonometric Functions

5-1 Angle Measure, Special Triangles, and Special Angles

5-2 Unit Circles and the Trigonometry of Real Numbers

5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

5-4 Graphs of Tangent and Cotangent Functions

5-5 Transformations and Applications of Trigonometric Graphs

5-6 The Trigonometry of Right Triangles

5-7 Trigonometry and the Coordinate Plane

Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1 Fundamental Identities and Families of Identities

6-2 Constructing and Verifying Identities

6-3 The Sum and Difference Identities

6-4 Double Angle, Half Angle & Product-to-Sum Identities

6-5 The Inverse Trigonometric Functions and Their Applications

6-6 Solving Basic Trigonometric Equations

6-7 General Trigonometric Equations and Applications

Chapter 7: Applications of Trigonometry

7-1 Oblique Triangles and the Law of Sines

7-2 The Law of Cosines; Area of a Triangle

7-3 Vectors and Vector Diagrams

7-4 Vector Applications and the Dot Product

7-5 Complex Numbers in Trigonometric Form

7-6 Demoivre’s Theorem and the Theorem on nth Roots

Chapter 8: Systems of Equations and Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Partial Fraction Decomposition

8-4 Systems of Inequalities and Linear Programming

8-5 Solving Systems Using Matrices and Row Operations

8-6 The Algebra of Matrices

8-7 Solving Linear Systems Using Matrix Equations

8-8 Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More

Chapter 9: Analytical Geometry

9-1 Introduction to Analytic Geometry

9-2 The Circle and the Ellipse

9-3 The Hyperbola

9-4 The Analytic Parabola

9-5 Nonlinear Systems of Equations and Inequalities

9-6 Polar Coordinates, Equations, and Graphs

9-7 More on Conic Sections: Rotation of Axes and Polar Form

9-8 Parametric Equations and Graphs

Chapter 10: Additional Topics in Algebra

10-1 Sequences and Series

10-2 Arithmetic Sequences

10-3 Geometric Sequences

10-4 Mathematical Induction

10-5 Counting Techniques

10-6 Introduction to Probability

10-7 The Binomial Theorem

Chapter 11: Bridges to Calculus - An Introduction to Limits

11-1 Finding Limits Numerically and Graphically

11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity

11-3 Infinite Limits and Limits at Infinity

11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

APPENDICES

A-1 A Review of Basic Concepts and Skills

A-2 US Standard Units and the Metric System

A-3 Rational Expressions and the Least Common Denominator

A-4 Deriving the Equation of a Conic

A-5 More on Matrices

A-6 Deriving the Equation of a Conic