大学代数与三角学(英文)

Index of Applications
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．S Factoring
Section R．6 Rational Expressions and More Operations on Radicals
Algebra for Calculus
Key Concepts
Review Exercises
Test

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
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

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
Key Concepts
Review Exercises
Test

CHAPTER 3 Cumulative Review Exercises
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
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

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
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 5 Trigonometric Functions
Section 53 Angles and Their Measure
Section 5．2 Right Triangle Trigonometry
Section 5．3 Trigonometric Functions of Any Angle
Section 5．4 Trigonometric Functions Defined on the Unit Circle
Section 5．5 Graphs of Sine and Cosine Functions
Section 5．6 Graphs of Other Trigonometric Functions
Problem Recognition Exercises： Comparing Graphical Characteristics of
Trigonometric Functions
Section 5．7 Inverse Trigonometric Functions
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 6 Analytic Trigonometry
Section 6．1 Fundamental Trigonometric Identities
Section 6．2 Sum and Difference Formulas
Section 6，3 Double-Angle， Power-Reducing， and
Half-Angle Formulas
Section 6．4 Product-to-Sum and Sum-to-Product Formulas
Section 6．5 Trigonometric Equations
Problem Recognition Exercises： Trigonometric Identities and Trigonometric Equations
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 7 Applications of Trigonometric Functions
Section 7．1 Applications of Right Triangles
Section 7．2 The Law of Sines
Section 7．3 The Law of Cosines
Problem Recognition Exercises： Solving Triangles Using a Variety of Tools
Section 7．4 Harmonic Motion
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 8 Trigonometry Applied to Polar Coordinate Systems and Vectors
Section 8．1 Polar Coordinates
Section 8．2 Graphs of Polar Equations
Problem Recognition Exercises； Comparing Equations in Polar and
Rectangular Form
Section 8．3 Complex Numbers in Polar Form
Section 8．4 Vectors
Section 8．5 Dot Product
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 9 Systems of Equations and Inequalities
Section 9．1 Systems of Linear Equations in
Two Variables and Applications
Section 9．2 Systems of Linear Equations in
Three Variables and Applications
Section 9．3 Partial Fraction Decomposition
Section 9．4 Systems of Nonlinear Equations in
Two Variables
Section 9．5 Inequalities and Systems of Inequalities in
Two Variables
Problem Recognition Exercises： Equations and Inequalities
in Two Variables
Section 9．6 Linear Programming
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 10 Matrices and Determinants and Applications
Section 10．1 Solving Systems of Linear Equations Using Matrices
Section 10．2 Inconsistent Systems and Dependent Equations
Section 10．3 Operations on Matrices
Section 10．4 Inverse Matrices and Matrix Equations
Section 10，5 Determinants and Cramer's Rule
Problem Recognition Exercises： Using Multiple Methods to Solve
Systems of Linear Equations
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 11 Analytic Geometry
Section 11．1 The Ellipse
Section 11．2 The Hyperbola
Section 11．3 The Parabola
Problem Recognition Exercises： Comparing Equations of Conic Sections and the General Equation
Section 11．4 Rotation of Axes
Section 11．5 Polar Equations of Conics
Section 11，6 Plane Curves and Parametric Equations
Key Concepts
Review Exercises
Test
Cumulative Review Exercises

CHAPTER 12 Sequences， Series， Induction， and Probability
Section 12．1 Sequences and Series
Section 12．2 Arithmetic Sequences and Series
Section 12．3 Geometric Sequences and Series
Problem Recognition Exercises： Comparing Arithmetic and Geometric
Sequences and Series
Section 12．4 Mathematical Induction
Section 12．5 The Binomial Theorem
Section 12．6 Principles of Counting
Section 12．7 Introduction to Probability
Key Concepts
Review Exercises
Test
Cumulative Review Exercises
Appendix A Additional Topics Appendix A-1
Student Answer Appendix SA-1
Credits C-1
Index I-1
编辑手记 E-1