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# Technical Mathematics, 6th Edition

**by**Paul A. Calter (Vermont Technical College); Michael A. Calter (Wesleyan University)

### 9780470534922

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## Summary

## Table of Contents

**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