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SectionR.1Sets and the Real Number Line
SectionR.2Integer Exponents and Scientific Notation
SectionR.3Rational Exponents and Radicals
SectionR.4Polynomials and Multiplication of Radicals
Problem Recognition Exercises Simplifying Algebraic Expressions
SectionR.5Factoring
SectionR.6Rational Expressions and More Operations on Radicals
Algebra for Calculus
Chapter 1:Equations and Inequalities
Section1.1Linear Equations and Rational Equations
Section1.2Applications with Linear and Rational Equations
Section1.3Complex Numbers
Section1.4Quadratic Equations
Problem Recognition Exercises Simplifying Expressions Versus Solving Equations
Section 1.5Applications of Quadratic Equations
Section1.6More Equations and Applications
Section1.7Linear, Compound, and Absolute Value Inequalities
Problem Recognition Exercises Recognizing and Solving Equations and Inequalities
Equations for Calculus
Chapter 2:Functions and Relations
Section2.1The Rectangular Coordinate System and Graphing Utilities
Section2.2Circles
Section2.3Functions and Relations
Section2.4Linear Equations in Two Variables and Linear Functions
Section2.5Applications of Linear Equations and Modeling
Problem Recognition Exercises Comparing Graphs of Equations
Section2.6Transformations of Graphs
Section2.7Analyzing Graphs of Functions and Piecewise-Defined Functions
Section2.8Algebra of Functions and Function Composition
Chapter 3:Polynomial and Rational Functions
Section3.1Quadratic Functions and Applications
Section3.2Introduction to Polynomial Functions
Section3.3Division of Polynomials and the Remainder and Factor Theorems
Section3.4Zeros of Polynomials
Section3.5Rational Functions
Problem Recognition Exercises Polynomial and Rational Functions
Section3.6Polynomial and Rational Inequalities
Problem Recognition Exercises Solving Equations and Inequalities
Section3.7Variation
Chapter 4:Exponential and Logarithmic Functions
Section4.1Inverse Functions
Section4.2Exponential Functions
Section4.3Logarithmic Functions
Problem Recognition Exercises Analyzing Functions
Section4.4Properties of Logarithms
Section4.5Exponential and Logarithmic Equations
Section4.6Modeling with Exponential and Logarithmic Functions
Chapter 5:Trigonometric Functions
Section5.1Angles and Their Measure
Section5.2Right Triangle Trigonometry
Section5.3Trigonometric Functions of Any Angle
Section5.4Trigonometric Functions Defined on the Unit Circle
Section5.5Graphs of Sine and Cosine Functions
Section5.6Graphs of Other Trigonometric Functions
Problem Recognition Exercises Comparing Graphical Characteristics of Trigonometric Functions
Section5.7Inverse Trigonometric Functions
Chapter 6:Analytic Trigonometry
Section6.1Fundamental Trigonometric Identities
Section6.2Sum and Difference Formulas
Section6.3Double-Angle and Half-Angle Formulas
Section6.4Product-to-Sum and Sum-to-Product Formulas
Section6.5Trigonometric Equations
Chapter 7:Applications of Trigonometric Functions
Section7.1Applications of Right Triangles
Section7.2The Law of Sines
Section7.3The Law of Cosines
Problem Recognition Exercises Solving Triangles Using a Variety of Tools
Section7.4Harmonic Motion and Combinations of Trigonometric Functions
Chapter 8:Trigonometry Applied to Rectangular and Polar Coordinate Systems and Vectors
Section8.1Polar Coordinates
Section8.2Graphs of Polar Equations
Problem Recognition Exercises Comparing Equations in Polar and Rectangular Form
Section 8.3Complex Numbers in Polar Form
Section8.4Vectors
Section8.5Dot Product
Chapter 9:Systems of Equations and Inequalities
Section9.1Systems of Linear Equations in Two Variables and Applications
Section9.2Systems of Linear Equations in Three Variables and Applications
Section9.3Partial Fraction Decomposition
Section9.4Systems of Nonlinear Equations in Two Variables
Section9.5Inequalities and Systems of Inequalities in Two Variables
Problem Recognition Exercises Equations and Inequalities in Two Variables
Section9.6Linear Programming
Chapter 10:Matrices and Determinants and Applications
Section10.1Solving Systems of Linear Equations Using Matrices
Section10.2Inconsistent Systems and Dependent Equations
Section10.3Operations on Matrices
Section10.4Inverse Matrices and Matrix Equations
Section10.5Determinants and Cramer's Rule
Problem Recognition Exercises Using Multiple Methods to Solve Systems of Linear Equations
Chapter 11:Analytic Geometry
Section11.1The Ellipse
Section11.2The Hyperbola
Section11.3The Parabola
Problem Recognition Exercises Comparing Equations of Conic Sections and General Equation
Section11.4Rotation of Axes
Section11.5Polar Equations of Conics
Section11.6Plane Curves and Parametric Equations
Chapter 12:Sequences, Series, Induction, and Probability
Section12.1Sequences and Series
Section12.2Arithmetic Sequences and Series
Section12.3Geometric Sequences and Series
Problem Recognition Exercises Comparing Arithmetic and Geometric Sequences and Series
Section12.4Mathematical Induction
Section12.5The Binomial Theorem
Section12.6Principles of Counting
Section12.7Introduction to Probability
Online:Section A-1Proof of the Binomial Theorem
A-2Definition of Conics From a Fixed Point and Fixed Line