Table of Contents
Chapter 1 – FUNCTIONS AND THEIR GRAPHS
- 1.1 Lines in the Plane
- 1.2 Functions
- 1.3 Graphs of Functions
- 1.4 Shifting, Reflecting, and Stretching Graphs
- 1.5 Combinations of Functions
- 1.6 Inverse Functions
- 1.7 Linear Models and Scatter Plots
Chapter 2 – POLYNOMIAL AND RATIONAL FUNCTIONS
- 2.1 Quadratic Functions
- 2.2 Polynomial Functions of Higher Degree
- 2.3 Real Zeros of Polynomial Functions
- 2.4 Complex Numbers
- 2.5 The Fundamental Theorem of Algebra
- 2.6 Rational Functions and Asymptotes
- 2.7 Graphs of Rational Functions
- 2.8 Quadratic Models
Chapter 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 Solving Exponential and Logarithmic Equations
- 3.5 Exponential and Logarithmic Models
- 3.6 Nonlinear Models
Chapter 4 – TRIGONOMETRIC FUNCTIONS
- 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
Chapter 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-Angle and Product-to-Sum Formulas
Chapter 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
Chapter 7 – LINEAR SYSTEMS AND MATRICES
- 7.1 Solving Systems of Equations
- 7.2 Systems of Linear Equations in Two Variables
- 7.3 Multivariable Linear Systems
- 7.4 Matrices and Systems of Equations
- 7.5 Operations with Matrices
- 7.6 The Inverse of a Square Matrix
- 7.7 The Determinant of a Square Matrix
- 7.8 Applications of Matrices and Determinants
Chapter 8 – SEQUENCES, SERIES, AND PROBABILITY
- 8.1 Sequences and Series
- 8.2 Arithmetic Sequences and Partial Sums
- 8.3 Geometric Sequences and Series
- 8.4 Mathematical Induction
- 8.5 The Binomial Theorem
- 8.6 Counting Principles
- 8.7 Probability
Chapter 9 – TOPICS IN ANALYTIC GEOMETRY
- 9.1 Circles and Parabolas
- 9.2 Ellipses
- 9.3 Hyperbolas
- 9.4 Rotation and Systems of Quadratic Equations
- 9.5 Parametric Equations
- 9.6 Polar Coordinates
- 9.7 Graphs of Polar Equations
- 9.8 Polar Equations of Conics
Chapter 10 – ANALYTIC GEOMETRY IN THREE DIMENSIONS
- 10.1 The Three-Dimensional Coordinate System
- 10.2 Vectors in Space
- 10.3 The Cross Product of Two Vectors
- 10.4 Lines and Planes in Space
Chapter 11 – LIMITS AND AN INTRODUCTION TO CALCULUS
- 11.1 Introduction to Limits
- 11.2 Techniques for Evaluating Limits
- 11.3 The Tangent Line Problem
- 11.4 Limits at Infinity and Limits of Sequences
- 11.5 The Area Problem
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