Sheldon Axler

Algebra & Trigonometry

With Student Solutions Manual

• Gebundenes Buch

Produktbeschreibung

Axler Algebra & Trigonometry is written for the two semester course. The text provides students with the skill and understanding needed for their coursework and for participating as an educated citizen in a complex society. Axler Algebra & Trigonometry focuses on depth, not breadth of topics by exploring necessary topics in greater detail. Readers will benefit from the straightforward definitions and plentiful examples of complex concepts. The Student Solutions Manual is integrated at the end of every section. The proximity of the solutions encourages students to go back and read the main text as they are working through the problems and exercises. The inclusion of the manual also saves students money. Axler Algebra & Trigonometry is available with WileyPLUS; an innovative, research-based, online environment for effective teaching and learning. WileyPLUS sold separately from text.

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Produktdetails

• Verlag: Wiley
• Seitenzahl: 784
• Erscheinungstermin: 8. März 2011
• Englisch
• Abmessung: 254mm x 203mm x 30mm
• Gewicht: 1451g
• ISBN-13: 9780470585795
• ISBN-10: 047058579X
• Artikelnr.: 33256829

Autorenporträt

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.

Inhaltsangabe

About the Author v
Preface to the Instructor xvi
WileyPLUS xxii
Acknowledgments xxiii
Preface to the Student xxvi
1 The Real Numbers 1
1.1 The Real Line 2
1.2 Algebra of the Real Numbers 7
1.3 Inequalities, Intervals, and Absolute Value 24
2 Combining Algebra and Geometry 41
2.1 The Coordinate Plane 42
2.2 Lines 57
2.3 Quadratic Expressions and Conic Sections 75
2.4 Area 98
3 Functions and Their Graphs 117
3.1 Functions 118
3.2 Function Transformations and Graphs 142
3.3 Composition of Functions 165
3.4 Inverse Functions 180
3.5 A Graphical Approach to Inverse Functions 197
4 Polynomial and Rational Functions 213
4.1 Integer Exponents 214
4.2 Polynomials 227
4.3 Rational Functions 245
4.4 Complex Numbers 262
5 Exponents and Logarithms 279
5.1 Exponents and Exponential Functions 280
5.2 Logarithms as Inverses of Exponential Functions 293
5.3 Applications of Logarithms 310
5.4 Exponential Growth 328
6 e and the Natural Logarithm 349
6.1 Defining e and ln 350
6.2 Approximations and area with e and ln 366
6.3 Exponential Growth Revisited 376
7 Systems of Equations 387
7.1 Equations and Systems of Equations 388
7.2 Solving Systems of Linear Equations 399
7.3 Solving Systems of Linear Equations Using Matrices 411
7.4 Matrix Algebra 424
8 Sequences, Series, and Limits 447
8.1 Sequences 448
8.2 Series 463
8.3 Limits 483
9 Trigonometric Functions 497
9.1 The Unit Circle 498
9.2 Radians 514
9.3 Cosine and Sine 529
9.4 More Trigonometric Functions 542
9.5 Trigonometry in Right Triangles 555
9.6 Trigonometric Identities 566
10 Trigonometric Algebra and Geometry 583
10.1 Inverse Trigonometric Functions 584
10.2 Inverse Trigonometric Identities 599
10.3 Using Trigonometry to Compute Area 613
10.4 The Law of Sines and the Law of Cosines 628
10.5 Double-Angle and Half-Angle Formulas 644
10.6 Addition and Subtraction Formulas 658
11 Applications of Trigonometry 671
11.1 Parametric Curves 672
11.2 Transformations of Trigonometric Functions 687
11.3 Polar Coordinates 705
11.4 Vectors 718
11.5 The Complex Plane 732
Photo Credits 743
Index 745

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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 Worked-out Solutions

1.3 Inequalities

Positive and Negative Numbers

Lesser and 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 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 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

Rat