Algebra and Trigonometry
, by Axler, Sheldon
- ISBN: 9780470470817 | 047047081X
- Cover: Paperback
- Copyright: 3/8/2011
College Algebra and Trigonometry will appeal to those who want to give important topics more in-depth, higher-level coverage. This text offers streamlined approach accompanied with accessible definitions across all chapters to allow for an easy-to-understand read. College Algebra contains prose that is precise, accurate, and easy to read, with straightforward definitions of even the topics that are typically most difficult for readers.
Sheldon Axler is well-known within the mathematics community. He has an Ivy League education, having received his AB in mathematics from Princeton in 1971, and his PhD in mathematics from UC Berkeley in 1975. Currently, Sheldon is the Dean of the College of Science and Engineering at SFSU. Previously, he held teaching positions at Michigan State, UC Berkeley, Indiana University, and MIT. He has received numerous grants, awards, and fellowships throughout his career. He regularly speaks at conferences and conventions and has done extensive writing in his discipline. Notably, he is the author of a successful textbook for the second course in linear Algebra, published with Springer and has held several editorial positions for mathematics journals and is currently a series editor for Springer.
As the author for Wiley's Precalculus: A Prelude to Calculus, Sheldon has shown himself an able and willing promoter of his title, garnering the interest of his colleagues nationwide and proving himself a valuable and responsive resource for our sales force.
| About the Author | |
| Preface to the Instructor | |
| Acknowledgments | |
| Preface to the Student | |
| The Real Numbers | |
| The Real Line | |
| Construction of the Real Line | |
| Is Every Real Number Rational? | |
| Problems | |
| 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 Worked-out Solutions | |
| Inequalities | |
| Positive and Negative Numbers | |
| Lesser and Greater | |
| Intervals | |
| Absolute Value | |
| Exercises, Problems, and Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Combining Algebra and Geometry | |
| The Coordinate Plane | |
| Coordinates | |
| Graphs of Equations | |
| Distance Between Two Points | |
| Length, Perimeter, and Circumference | |
| Exercises, Problems, and Worked-out Solutions | |
| Lines | |
| Slope | |
| The Equation of a Line | |
| Parallel Lines | |
| Perpendicular Lines | |
| Midpoints | |
| Exercises, Problems, and Worked-out Solutions | |
| Quadratic Expressions and Conic Sections | |
| Completing the Square | |
| The Quadratic Formula | |
| Circles | |
| Ellipses | |
| Parabolas | |
| Hyperbolas | |
| Exercises, Problems, and Worked-out Solutions | |
| Area | |
| Squares, Rectangles, and Parallelograms | |
| Triangles and Trapezoids | |
| Stretching | |
| Circles and Ellipses | |
| Exercises, Problems, and Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Functions and Their Graphs | |
| 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 Worked-out Solutions | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| Polynomial and Rational Functions | |
| Integer Exponents | |
| Positive Integer Exponents | |
| Properties of Exponents | |
| Defining x0 | |
| Negative Integer Exponents | |
| Manipulations with Exponents | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 | |
| 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 | |
| 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 | |
| Exponents and Logarithms | |
| Exponents and Exponential Functions | |
| Roots | |
| Rational Exponents | |
| Real Exponents | |
| Exponential Functions | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 | |
| 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 Worked-out Solutions | |
| Exponential Growth | |
| Functions with Exponential Growth | |
| Population Growth | |
| Compound Interest | |
| Exercises, Problems, and Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| e and the Natural Logarithm | |
| 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 | |
| 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 | |
| Exponential Growth Revisited | |
| Continuously Compounded Interest | |
| Continuous Growth Rates | |
| Doubling Your Money | |
| Exercises, Problems, and Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Trigonometric Functions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Trigonometric Algebra and Geometry | |
| Inverse Trigonometric Functions | |
| The Arccosine Function | |
| The Arcsine Function | |
| The Arctangent Function | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| Double-Angle and Half-Angle 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 Worked-out Solutions | |
| 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 Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Applications of Trigonometry | |
| Parametric Curves | |
| Curves in the Coordinate Plane | |
| Graphing Inverse Functions as Parametric Curves | |
| Shifting, Stretching, or Flipping a Parametric Curve | |
| Exercises, Problems, and Worked-out Solutions | |
| Transformations of Trigonometric Functions | |
| Amplitude | |
| Period | |
| Phase Shift | |
| Exercises, Problems, and Worked-out Solutions | |
| Polar Coordinates | |
| Defining Polar Coordinates | |
| Converting from Polar to Rectangular Coordinates | |
| Converting from Rectangular to Polar Coordinates | |
| Graphs of Polar Equations | |
| Exercises, Problems, and Worked-out Solutions | |
| Vectors | |
| An Algebraic and Geometric Introduction to Vectors | |
| Vector Addition | |
| Vector Subtraction | |
| The Dot Product | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 Worked-out Solutions | |
| Chapter Summary and Chapter Review Questions | |
| Systems of Equations and Inequalities | |
| Equations and Systems of Equations | |
| Solving an Equation | |
| Solving a System of Equations | |
| Systems of Linear Equations | |
| Matrices | |
| Exercises, Problems, and Worked-out Solutions | |
| Solving Systems of Linear Equations | |
| Gaussian Elimination | |
| Gaussian Elimination with Matrices | |
| Special Cases-No Solutions | |
| Special Cases-Infinitely Many Solutions | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 | |
| Sequences, Series, and Limits | |
| Sequences | |
| Introduction to Sequences | |
| Arithmetic Sequences | |
| Geometric Sequences | |
| Recursively-Defined Sequences | |
| Exercises, Problems, and Worked-out Solutions | |
| Series | |
| Sums of Sequences | |
| Arithmetic Series | |
| Geometric Series | |
| Summation Notation | |
| The Binomial Theorem | |
| Exercises, Problems, and Worked-out Solutions | |
| 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 | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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