Chapter R: Review of Prerequisites

Section R.1 Sets and the Real Number Line

Section R.2 Integer Exponents and Scientific Notation

Section R.3 Rational Exponents and Radicals

Section R.4 Polynomials and Multiplication of Radicals

Problem Recognition Exercises: Simplifying Algebraic Expressions

Section R.5 Factoring

Section R.6 Rational Expressions and More Operations on Radicals

Algebra for Calculus

Chapter 1: Equations and Inequalities

Section 1.1 Linear Equations and Rational Equations

Section 1.2 Applications with Linear and Rational Equations

Section 1.3 Complex Numbers

Section 1.4 Quadratic Equations

Problem Recognition Exercises: Simplifying Expressions Versus Solving Equations

Section 1.5 Applications of Quadratic Equations

Section 1.6 More Equations and Applications

Section 1.7 Linear, Compound, and Absolute Value Inequalities

Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities

Equations and Inequalities for Calculus

Chapter 2: Functions and Relations

Section 2.1 The Rectangular Coordinate System and Graphing Utilities

Section 2.2 Circles

Section 2.3 Functions and Relations

Section 2.4 Linear Equations in Two Variables and Linear Functions

Section 2.5 Applications of Linear Equations and Modeling

Problem Recognition Exercises: Comparing Graphs of Equations

Section 2.6 Transformations of Graphs

Section 2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions

Section 2.8 Algebra of Functions and Function Composition

Chapter 3: Polynomial and Rational Functions

Section 3.1 Quadratic Functions and Applications

Section 3.2 Introduction to Polynomial Functions

Section 3.3 Division of Polynomials and the Remainder and Factor Theorems

Section 3.4 Zeros of Polynomials

Section 3.5 Rational Functions

Problem Recognition Exercises: Polynomial and Rational Functions

Section 3.6 Polynomial and Rational Inequalities

Problem Recognition Exercises: Solving Equations and Inequalities

Section 3.7 Variation

Chapter 4: Exponential and Logarithmic Functions

Section 4.1 Inverse Functions

Section 4.2 Exponential Functions

Section 4.3 Logarithmic Functions

Problem Recognition Exercises: Analyzing Functions

Section 4.4 Properties of Logarithms

Section 4.5 Exponential and Logarithmic Equations and Applications

Section 4.6 Modeling with Exponential and Logarithmic Functions

Chapter 5: Systems of Equations and Inequalities

Section 5.1 Systems of Linear Equations in Two Variables and Applications

Section 5.2 Systems of Linear Equations in Three Variables and Applications

Section 5.3 Partial Fraction Decomposition

Section 5.4 Systems of Nonlinear Equations in Two Variables

Section 5.5 Inequalities and Systems of Inequalities in Two Variables

Problem Recognition Exercises: Equations and Inequalities in Two Variables

Section 5.6 Linear Programming

Chapter 6: Matrices and Determinants and Applications

Section 6.1 Solving Systems of Linear Equations Using Matrices

Section 6.2 Inconsistent Systems and Dependent Equations

Section 6.3 Operations on Matrices

Section 6.4 Inverse Matrices and Matrix Equations

Section 6.5 Determinants and Cramer’s Rule

Problem Recognition Exercises: Using Multiple Methods to Solve Systems of Linear Equations

Chapter 7: Analytic Geometry

Section 7.1 The Ellipse

Section 7.2 The Hyperbola

Section 7.3 The Parabola

Problem Recognition Exercises: Comparing Equations of Conic Sections and the General Equation

Chapter 8: Sequences, Series, Induction, and Probability

Section 8.1 Sequences and Series

Section 8.2 Arithmetic Sequences and Series

Section 8.3 Geometric Sequences and Series

Problem Recognition Exercises: Comparing Arithmetic and Geometric Sequences and Series

Section 8.4 Mathematical Induction

Section 8.5 The Binomial Theorem

Section 8.6 Principles of Counting

Section 8.7 Introduction to Probability

Appendix A: Additional Topics Appendix (Online only)