College algebra

INDICE: About the Author v Preface to the Instructor xiii Acknowledgments xvii Preface to the Student xx 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 OperationsThe Distributive Property Additive Inverses and Subtraction Multiplicative Inverses and the Algebra of Fractions Symbolic Calculators Exercises, Problems, and Worked-out Solutions 1.3 Inequalities Positive and Negative Numbers Lesserand Greater Intervals Absolute Value Exercises, Problems, and Worked-out 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 Worked-out Solutions 2.2 Lines Slope The Equation of a Line Parallel Lines Perpendicular Lines Midpoints Exercises, Problems, and Worked-out Solutions 2.3 Quadratic Expressions and Conic Sections Completing the Square The Quadratic Formula Circles Ellipses Parabolas Hyperbolas Exercises, Problems, and Worked-out Solutions 2.4 Area Squares, Rectangles, and Parallelograms Triangles and Trapezoids Stretching Circles and Ellipses Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions 3 Functions and Their Graphs3.1 Functions Definition and Examples The Graph of a Function The Domain of aFunction The Range of a Function Functions via Tables Exercises, Problems, and Worked-out 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 Worked-out 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 Worked-out Solutions 3.4 Inverse Functions The Inverse Problem One-to-one 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 Worked-out Solutions 3.5 A Graphical Approach to Inverse Functions The Graph of an Inverse Function Graphical Interpretation of One-to-One Increasing and Decreasing Functions Inverse Functions via Tables Exercises, Problems, and Worked-out 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 Worked-out 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 Worked-out 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 Worked-out 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 Worked-out 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 Worked-out 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 Half-Life Exercises, Problems, and Worked-out Solutions 5.3 Applications of Logarithms Logarithm of a Product Logarithmof a Quotient Earthquakes and the Richter Scale Sound Intensity and Decibels Star Brightness and Apparent Magnitude Change of Base Exercises, Problems, andWorked-out Solutions 5.4 Exponential Growth Functions with Exponential GrowthPopulation Growth Compound Interest Exercises, Problems, and Worked-out 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 Worked-out 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 Worked-out Solutions 6.3 Exponential Growth Revisited Continuously Compounded Interest Continuous Growth Rates Doubling Your Money Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions 7 Systems of Equations and Inequalities 7.1 Equations and Systems of Equations Solving an Equation Solving a System of Equations Systems of Linear Equations Matrices Exercises, Problems, and Worked-out Solutions 7.2 Solving Systems of Linear Equations Gaussian Elimination Gaussian Elimination with Matrices Special Cases--NoSolutions Special Cases--Infinitely Many Solutions Exercises, Problems, and Worked-out Solutions 7.3 Matrix Algebra Adding and Subtracting Matrices Multiplying Matrices The Inverse of a Matrix Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions 8 Sequences, Series, and Limits 8.1 Sequences Introduction to Sequences Arithmetic Sequences Geometric Sequences Recursively-Defined Sequences Exercises, Problems, and Worked-out Solutions 8.2 Series Sums of Sequences Arithmetic Series Geometric Series Summation Notation The Binomial Theorem Exercises, Problems, and Worked-out Solutions 8.3 Limits Introduction to Limits Infinite Series Decimals as Infinite Series Special Infinite Series Exercises, Problems, and Worked-out Solutions Chapter Summary and Chapter Review Questions

• ISBN: 978-0-470-47077-0
• Editorial: John Wiley & Sons
• Encuadernacion: Rústica
• Páginas: 624
• Fecha Publicación: 26/11/2010
• Nº Volúmenes: 1
• Idioma: Inglés