This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.

**1** **Review of Numerical Computation 1****1–1** The Real Numbers 2

**1–2** Addition and Subtraction 9

**1–3** Multiplication 15

**1–4** Division 19

**1–5** Powers and Roots 23

**1–6** Combined Operations 29

**1–7** Scientific Notation and Engineering Notation 32

**1–8** Units of Measurement 41

**1–9** Percentage 51

Chapter 1 Review Problems 59

**2** **Introduction to Algebra 62**

**2–1** Algebraic Expressions 63

**2–2** Adding and Subtracting Polynomials 67

**2–3** Laws of Exponents 72

**2–4** Multiplying a Monomial by a Monomial 80

**2–5** Multiplying a Monomial and a Multinomial 83

**2–6** Multiplying a Binomial by a Binomial 86

**2–7** Multiplying a Multinomial by a Multinomial 88

**2–8** Raising a Multinomial to a Power 90

**2–9** Dividing a Monomial by a Monomial 92

**2–10** Dividing a Polynomial by a Monomial 95

**2–11** Dividing a Polynomial by a Polynomial 98

Chapter 2 Review Problems 101

**3** **Simple Equations and Word Problems 103**

**3–1** Solving a Simple Equation 104

**3–2** Solving Word Problems 113

**3–3** Uniform Motion Applications 118

**3–4** Money Problems 121

**3–5** Applications Involving Mixtures 123

**3–6** Statics Applications 127

**3–7** Applications to Work, Fluid Flow, and Energy Flow 129

Chapter 3 Review Problems 133

**4** **Functions 136**

**4–1** Functions and Relations 137

**4–2** More on Functions 144

Chapter 4 Review Problems 154

**5** **Graphs 156**

**5–1** Rectangular Coordinates 157

**5–2** Graphing an Equation 161

**5–3** Graphing a Function by Calculator 164

**5–4** The Straight Line 167

**5–5** Solving an Equation Graphically 172

Chapter 5 Review Problems 173

**6 Geometry 175**

**6–1** Straight Lines and Angles 176

**6–2** Triangles 180

**6–3** Quadrilaterals 187

**6–4** The Circle 190

**6–5** Polyhedra 196

**6–6** Cylinder, Cone, and Sphere 201

Chapter 6 Review Problems 205

**7** **Right Triangles and Vectors 207**

**7–1** The Trigonometric Functions 208

**7–2** Solution of Right Triangles 212

**7–3** Applications of the Right Triangle 216

**7–4** Angles in Standard Position 221

**7–5** Introduction to Vectors 222

**7–6** Applications of Vectors 226

Chapter 7 Review Problems 229

**8** **Oblique Triangles and Vectors 231**

**8–1** Trigonometric Functions of Any Angle 232

**8–2** Finding the Angle When the Trigonometric Function Is Known 236

**8–3** Law of Sines 240

**8–4** Law of Cosines 246

**8–5** Applications 251

**8–6** Non-Perpendicular Vectors 255

Chapter 8 Review Problems 260

**9** **Systems of Linear Equations 263**

**9–1** Systems of Two Linear Equations 264

**9–2** Applications 270

**9–3** Other Systems of Equations 279

**9–4** Systems of Three Equations 284

Chapter 9 Review Problems 290

**10** **Matrices and Determinants 292**

**10–1** Introduction to Matrices 293

**10–2** Solving Systems of Equations by the Unit Matrix Method 297

**10–3** Second-Order Determinants 302

**10–4** Higher-Order Determinants 308

Chapter 10 Review Problems 316

**11** **Factoring and Fractions 319**

**11–1** Common Factors 320

**11–2** Difference of Two Squares 323

**11–3** Factoring Trinomials 326

**11–4** Other Factorable Expressions 333

**11–5** Simplifying Fractions 335

**11–6** Multiplying and Dividing Fractions 340

**11–7** Adding and Subtracting Fractions 344

**11–8** Complex Fractions 349

**11–9** Fractional Equations 352

**11–10** Literal Equations and Formulas 355

Chapter 11 Review Problems 360

**12 Quadratic Equations 363**

**12–1** Solving a Quadratic Equation Graphically and by Calculator 364

**12–2** Solving a Quadratic by Formula 368

**12–3** Applications 372

Chapter 12 Review Problems 377

**13** **Exponents and Radicals 379**

**13–1** Integral Exponents 380

**13–2** Simplification of Radicals 385

**13–3** Operations with Radicals 392

**13–4** Radical Equations 398

Chapter 13 Review Problems 403

**14** **Radian Measure, Arc Length, and Rotation 405**

**14–1** Radian Measure 406

**14–2** Arc Length 413

**14–3** Uniform Circular Motion 416

Chapter 14 Review Problems 420

**15** **Trigonometric, Parametric, and Polar Graphs 422**

**15–1** Graphing the Sine Wave by Calculator 423

**15–2** Manual Graphing of the Sine Wave 430

**15–3** The Sine Wave as a Function of Time 435

**15–4** Graphs of the Other Trigonometric Functions 441

**15–5** Graphing a Parametric Equation 448

**15–6** Graphing in Polar Coordinates 452

Chapter 15 Review Problems 459

**16** **Trigonometric Identities and Equations 461**

**16–1** Fundamental Identities 462

**16–2** Sum or Difference of Two Angles 469

**16–3** Functions of Double Angles and Half-Angles 474

**16–4** Evaluating a Trigonometric Expression 481

**16–5** Solving a Trigonometric Equation 484

Chapter 16 Review Problems 489

**17** **Ratio, Proportion, and Variation 491**

**17–1** Ratio and Proportion 492

**17–2** Similar Figures 497

**17–3** Direct Variation 501

**17–4** The Power Function 505

**17–5** Inverse Variation 509

**17–6** Functions of More Than One Variable 513

Chapter 17 Review Problems 518

**18** **Exponential and Logarithmic Functions 521**

**18–1** The Exponential Function 522

**18–2** Logarithms 532

**18–3** Properties of Logarithms 539

**18–4** Solving an Exponential Equation 547

**18–5** Solving a Logarithmic Equation 554

Chapter 18 Review Problems 560

**19 Complex Numbers 562**

**19–1** Complex Numbers in Rectangular Form 563

**19–2** Complex Numbers in Polar Form 568

**19–3** Complex Numbers on the Calculator 572

**19–4** Vector Operations Using Complex Numbers 575

**19–5** Alternating Current Applications 578

Chapter 19 Review Problems 584

**20** **Sequences, Series, and the Binomial Theorem 586**

**20–1** Sequences and Series 587

**20–2** Arithmetic and Harmonic Progressions 593

**20–3** Geometric Progressions 600

**20–4** Infinite Geometric Progressions 604

**20–5** The Binomial Theorem 607

Chapter 20 Review Problems 614

**21** **Introduction to Statistics and Probability 617**

**21–1** Definitions and Terminology 618

**21–2** Frequency Distributions 622

**21–3** Numerical Description of Data 628

**21–4** Introduction to Probability 638

**21–5** The Normal Curve 648

**21–6** Standard Errors 654

**21–7** Process Control 661

**21–8** Regression 669

Chapter 21 Review Problems 674

**22** **Analytic Geometry 679**

**22–1** The Straight Line 680

**22–2** Equation of a Straight Line 687

**22–3** The Circle 694

**22–4** The Parabola 702

**22–5** The Ellipse 713

**22–6** The Hyperbola 725

Chapter 22 Review Problems 733

Appendices

**A** Summary of Facts and Formulas A-0

**B** Conversion Factors A-0

**C** Table of Integrals A-0

**Indexes**

Applications Index I-0

Index to Writing Questions I-0

Index to Projects I-0

General Index I-0