## Precalculus: Mathematics for Calculus, Eighth Edition

By James Stewart, Lothar Redlin and Saleem Watson

**Contents:**

Preface x

A Tribute to Lothar Redlin xvii

To the Student xviii

Technology in the Eighth Edition xix

Prologue: Principles of Problem Solving P1

1 Fundamentals 1

Chapter Overview 1

1.1 Real Numbers 2

1.2 Exponents and Radicals 13

1.3 Algebraic Expressions 25

1.4 Rational Expressions 36

1.5 Equations 45

1.6 Complex Numbers 59

1.7 Modeling with Equations 65

1.8 Inequalities 81

1.9 The Coordinate Plane; Graphs of Equations; Circles 92

1.10 **Lines** 106

1.11 Solving Equations and Inequalities Graphically 117

1.12 Modeling Variation 124

Chapter 1 Review 131

Chapter 1 Test 139

■ Focus on Modeling Fitting Lines to Data 141

2 Functions 147

Chapter Overview 147

2.1 Functions 148

2.2 Graphs of Functions 159

2.3 Getting Information from the Graph of a Function 172

2.4 Average Rate of Change of a Function 185

2.5 Linear Functions and Models 193

2.6 Transformations of Functions 201

2.7 Combining Functions 214

2.8 One-to-One Functions and Their Inverses 224

Chapter 2 Chapter 2 Review 234

Chapter 2 Test 241

■ Focus on Modeling Modeling with Functions 243

3 Polynomial and Rational Functions 251

Chapter Overview 251

3.1 Quadratic Functions and Models 252

3.2 Polynomial Functions and Their Graphs 260

3.3 Dividing Polynomials 275

3.4 Real Zeros of Polynomials 281

3.5 Complex Zeros and the Fundamental Theorem of Algebra 293

3.6 Rational Functions 301

3.7 Polynomial and Rational Inequalities 318

Chapter 3 Review 324

Chapter 3 Test 330

■ Focus on Modeling Fitting Polynomial Curves to Data 332

4 Exponential and Logarithmic Functions 337

Chapter Overview 337

Chapte4.1 Exponential Functions 338

4.2 The Natural Exponential Function 346

4.3 Logarithmic Functions 352

4.4 Laws of Logarithms 362

4.5 Exponential and Logarithmic Equations 369

4.6 Modeling with Exponential Functions 379

4.7 Logarithmic Scales 391

Chapter 4 Review 396

Chapter 4 Test 402

■ Focus on Modeling Fitting Exponential and Power Curves to Data 403

Cumulative Review Test: Chapters 2, 3, and 4 (Website)

5 Trigonometric Functions: Unit Circle Approach 409

Chapter Overview 409

5.1 The Unit Circle 410

5.2 Trigonometric Functions of Real Numbers 417

5.3 Trigonometric Graphs 427

5.4 More Trigonometric Graphs 442

5.5 Inverse Trigonometric Functions and Their Graphs 451

5.6 Modeling Harmonic Motion 458

Chapter 5 Review 472

Chapter 5 Test 478

■ Focus on Modeling Fitting Sinusoidal Curves to Data 479

6 Trigonometric Functions: Right Triangle Approach 485

Chapter Overview 485

6.1 Angle Measure 486

6.2 Trigonometry of Right Triangles 496

6.3 Trigonometric Functions of Angles 505

6.4 Inverse Trigonometric Functions and Right Triangles 516

6.5 The Law of Sines 524

6.6 The Law of Cosines 532

Chapter 6 Review 540

Chapter 6 Test 547

■ Focus on Modeling Surveying 549

7 Analytic Trigonometry 553

Chapter Overview 553

7.1 Trigonometric Identities 554

7.2 Addition and Subtraction Formulas 561

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas 570

7.4 Basic Trigonometric Equations 580

7.5 More Trigonometric Equations 586

Chapter 7 Review 592

Chapter 7 Test 597

■ Focus on Modeling Traveling and Standing Waves 598

Cumulative Review Test: Chapters 5, 6, and 7 (Website)

8 Polar Coordinates, Parametric Equations,

and Vectors 603

Chapter Overview 603

8.1 Polar Coordinates 604

8.2 Graphs of Polar Equations 610

8.3 Polar Form of Complex Numbers; De Moivre’s Theorem 618

8.4 Plane Curves and Parametric Equations 628

8.5 Vectors 637

8.6 The Dot Product 647

Chapter 8 Review 655

Chapter 8 Test 659

■ Focus on Modeling The Path of a Projectile 661

9 Systems of Equations and Inequalities 665

Chapter Overview 665

9.1 Systems of Linear Equations in Two Variables 666

9.2 Systems of Linear Equations in Several Variables 677

9.3 Matrices and Systems of Linear Equations 685

9.4 The Algebra of Matrices 698

9.5 Inverses of Matrices and Matrix Equations 708

9.6 Determinants and Cramer’s Rule 718

9.7 Partial Fractions 729

9.8 Systems of Nonlinear Equations 735

9.9 Systems of Inequalities 740

Chapter 9 Review 750

Chapter 9 Test 757

■ Focus on Modeling Linear Programming 759

10 Conic Sections 765

Chapter Overview 765

10.1 Parabolas 766

10.2 Ellipses 775

10.3 Hyperbolas 784

10.4 Shifted Conics 792

10.5 Rotation of Axes 802

10.6 Polar Equations of Conics 810

Chapter 10 Review 816

Chapter 10 Test 821

■ Focus on Modeling Conics in Architecture 822

Cumulative Review Test: Chapters 8, 9, and 10 (Website)

11 Sequences and Series 827

Chapter Overview 827

11.1 Sequences and Summation Notation 828

11.2 Arithmetic Sequences 838

11.3 Geometric Sequences 844

11.4 Mathematical Induction 853

11.5 The Binomial Theorem 859

Chapter 11 Review 867

Chapter 11 Test 871

■ Focus on Modeling Modeling with Recursive Sequences 872

12 Limits: A Preview of Calculus 877

Chapter Overview 877

12.1 Finding Limits Numerically and Graphically 878

12.2 Finding Limits Algebraically 886

12.3 Tangent Lines and Derivatives 894

12.4 Limits at Infinity; Limits of Sequences 904

12.5 Areas 912

Chapter 12 Review 920

Chapter 12 Test 924

■ Focus on Modeling Interpretations of Area 925

Cumulative Review Test: Chapters 11 and 12 (Website)

Appendix A Geometry Review 929

Appendix B Calculations and Significant Figures (Website)

Appendix C Graphing with a Graphing Calculator (Website)

Appendix D Using the TI-83/84 Graphing Calculator (Website)

Appendix E Three-Dimensional Coordinate Geometry (Website)

Appendix F Mathematics of Finance (Website)

Appendix G Probability and Statistics (Website)

Answers A1

Index I1