Contents
About the Author Preface to the Instructor Acknowledgments Preface to the Student 1 The Real Numbers 1.1 The Real Line Construction of the Real Line Is Every Real Number Rational? Problems 1.2 Algebra of the Real Numbers Commutativity and Associativity The Order of Algebraic Operations The Distributive Property Additive Inverses and Subtraction Multiplicative Inverses and the Algebra of Fractions Symbolic Calculators Exercises, Problems, and Workedout Solutions 1.3 Inequalities Positive and Negative Numbers Lesser and Greater Intervals Absolute Value Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 2 Combining Algebra and Geometry 2.1 The Coordinate Plane Coordinates Graphs of Equations Distance Between Two Points Length, Perimeter, and Circumference Exercises, Problems, and Workedout Solutions 2.2 Lines Slope The Equation of a Line Parallel Lines Perpendicular Lines Midpoints Exercises, Problems, and Workedout Solutions 2.3 Quadratic Expressions and Conic Sections Completing the Square The Quadratic Formula Circles Ellipses Parabolas Hyperbolas Exercises, Problems, and Workedout Solutions 2.4 Area Squares, Rectangles, and Parallelograms Triangles and Trapezoids Stretching Circles and Ellipses Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 3 Functions and Their Graphs 3.1 Functions Definition and Examples The Graph of a Function The Domain of a Function The Range of a Function Functions via Tables Exercises, Problems, and Workedout Solutions 3.2 Function Transformations and Graphs Vertical Transformations: Shifting, Stretching, and Flipping Horizontal Transformations: Shifting, Stretching, Flipping Combinations of Vertical Function Transformations Even Functions Odd Functions Exercises, Problems, and Workedout Solutions 3.3 Composition of Functions Combining Two Functions Definition of Composition Order Matters in Composition Decomposing Functions Composing More than Two Functions Function Transformations as Compositions Exercises, Problems, and Workedout Solutions 3.4 Inverse Functions The Inverse Problem Onetoone Functions The Definition of an Inverse Function The Domain and Range of an Inverse Function The Composition of a Function and Its Inverse Comments about Notation Exercises, Problems, and Workedout Solutions 3.5 A Graphical Approach to Inverse Functions The Graph of an Inverse Function Graphical Interpretation of OnetoOne Increasing and Decreasing Functions Inverse Functions via Tables Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 4 Polynomial and Rational Functions 4.1 Integer Exponents Positive Integer Exponents Properties of Exponents Defining x0 Negative Integer Exponents Manipulations with Exponents Exercises, Problems, and Workedout Solutions 4.2 Polynomials The Degree of a Polynomial The Algebra of Polynomials Zeros and Factorization of Polynomials The Behavior of a Polynomial Near 1 Graphs of Polynomials Exercises, Problems, and Workedout Solutions 4.3 Rational Functions Ratios of Polynomials The Algebra of Rational Functions Division of Polynomials The Behavior of a Rational Function Near 1 Graphs of Rational Functions Exercises, Problems, and Workedout Solutions 4.4 Complex Numbers The Complex Number System Arithmetic with Complex Numbers Complex Conjugates and Division of Complex Numbers Zeros and Factorization of Polynomials, Revisited Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 5 Exponents and Logarithms 5.1 Exponents and Exponential Functions Roots Rational Exponents Real Exponents Exponential Functions Exercises, Problems, and Workedout Solutions 5.2 Logarithms as Inverses of Exponential Functions Logarithms Base 2 Logarithms with Any Base Common Logarithms and the Number of Digits Logarithm of a Power Radioactive Decay and HalfLife Exercises, Problems, and Workedout Solutions 5.3 Applications of Logarithms Logarithm of a Product Logarithm of a Quotient Earthquakes and the Richter Scale Sound Intensity and Decibels Star Brightness and Apparent Magnitude Change of Base Exercises, Problems, and Workedout Solutions 5.4 Exponential Growth Functions with Exponential Growth Population Growth Compound Interest Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 6 e and the Natural Logarithm 6.1 Defining e and ln Estimating Area Using Rectangles Defining e Defining the Natural Logarithm Properties of the Exponential Function and ln Exercises, Problems, and Workedout Solutions 6.2 Approximations with e and ln Approximation of the Natural Logarithm Inequalities with the Natural Logarithm Approximations with the Exponential Function An Area Formula Exercises, Problems, and Workedout Solutions 6.3 Exponential Growth Revisited Continuously Compounded Interest Continuous Growth Rates Doubling Your Money Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 7 Trigonometric Functions 7.1 The Unit Circle The Equation of the Unit Circle Angles in the Unit Circle Negative Angles Angles Greater Than 360 Length of a Circular Arc Special Points on the Unit Circle Exercises, Problems, and Workedout Solutions 7.2 Radians A Natural Unit of Measurement for Angles Negative Angles Angles Greater Than 2 Length of a Circular Arc Area of a Slice Special Points on the Unit Circle Exercises, Problems, and Workedout Solutions 7.3 Cosine and Sine Definition of Cosine and Sine Cosine and Sine of Special Angles The Signs of Cosine and Sine The Key Equation Connecting Cosine and Sine The Graphs of Cosine and Sine Exercises, Problems, and Workedout Solutions 7.4 More Trigonometric Functions Definition of Tangent Tangent of Special Angles The Sign of Tangent Connections between Cosine, Sine, and Tangent The Graph of Tangent Three More Trigonometric Functions Exercises, Problems, and Workedout Solutions 7.5 Trigonometry in Right Triangles Trigonometric Functions via Right Triangles Two Sides of a Right Triangle One Side and One Angle of a Right Triangle Exercises, Problems, and Workedout Solutions 7.6 Trigonometric Identities The Relationship Between Cosine and Sine Trigonometric Identities for the Negative of an Angle Trigonometric Identities with Trigonometric Identities Involving a Multiple of Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 8 Trigonometric Algebra and Geometry 8.1 Inverse Trigonometric Functions The Arccosine Function The Arcsine Function The Arctangent Function Exercises, Problems, and Workedout Solutions 8.2 Inverse Trigonometric Identities The Arccosine, Arcsine, and Arctangent of t: Graphical Approach The Arccosine, Arcsine, and Arctangent of t: Algebraic Approach Arccosine Plus Arcsine The Arctangent of 1t Composition of Trigonometric Functions and Their Inverses More Compositions with Inverse Trigonometric Functions Exercises, Problems, and Workedout Solutions 8.3 Using Trigonometry to Compute Area The Area of a Triangle via Trigonometry Ambiguous Angles The Area of a Parallelogram via Trigonometry The Area of a Polygon Exercises, Problems, and Workedout Solutions 8.4 The Law of Sines and the Law of Cosines The Law of Sines Using the Law of Sines The Law of Cosines Using the Law of Cosines When to Use Which Law Exercises, Problems, and Workedout Solutions 8.5 DoubleAngle and HalfAngle Formulas The Cosine of 2 The Sine of 2 The Tangent of 2 The Cosine and Sine of 2 The Tangent of 2 Exercises, Problems, and Workedout Solutions 8.6 Addition and Subtraction Formulas The Cosine of a Sum and Difference The Sine of a Sum and Difference The Tangent of a Sum and Difference Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 9 Applications of Trigonometry 9.1 Parametric Curves Curves in the Coordinate Plane Graphing Inverse Functions as Parametric Curves Shifting, Stretching, or Flipping a Parametric Curve Exercises, Problems, and Workedout Solutions 9.2 Transformations of Trigonometric Functions Amplitude Period Phase Shift Exercises, Problems, and Workedout Solutions 9.3 Polar Coordinates Defining Polar Coordinates Converting from Polar to Rectangular Coordinates Converting from Rectangular to Polar Coordinates Graphs of Polar Equations Exercises, Problems, and Workedout Solutions 9.4 Vectors An Algebraic and Geometric Introduction to Vectors Vector Addition Vector Subtraction The Dot Product Exercises, Problems, and Workedout Solutions 9.5 The Complex Plane Complex Numbers as Points in the Plane Geometric Interpretation of Complex Multiplication and Division De Moivre's Theorem Finding Complex Roots Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 10 Systems of Equations and Inequalities 10.1 Equations and Systems of Equations Solving an Equation Solving a System of Equations Systems of Linear Equations Matrices Exercises, Problems, and Workedout Solutions 10.2 Solving Systems of Linear Equations Gaussian Elimination Gaussian Elimination with Matrices Special CasesNo Solutions Special CasesInfinitely Many Solutions Exercises, Problems, and Workedout Solutions 10.3 Matrix Algebra Adding and Subtracting Matrices Multiplying Matrices The Inverse of a Matrix Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions 11 Sequences, Series, and Limits 11.1 Sequences Introduction to Sequences Arithmetic Sequences Geometric Sequences RecursivelyDefined Sequences Exercises, Problems, and Workedout Solutions 11.2 Series Sums of Sequences Arithmetic Series Geometric Series Summation Notation The Binomial Theorem Exercises, Problems, and Workedout Solutions 11.3 Limits Introduction to Limits Infinite Series Decimals as Infinite Series Special Infinite Series Exercises, Problems, and Workedout Solutions Chapter Summary and Chapter Review Questions
Product Details

publication date:
10/05/2011

ISBN13:
9780470470817

Format:
Paperback

Number Of Pages:
784
 ID: 9780470470817

weight:
1246

ISBN10:
047047081X
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