Technical Mathematics, 6th Edition

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