Textbook

# Technical Mathematics, 6th Edition

## Description

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.

See More

1 Review of Numerical Computation 1

1–1 The Real Numbers 2

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

6–4 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

12–1 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

13–1 Integral Exponents 380

Chapter 13 Review Problems 403

14 Radian Measure, Arc Length, and Rotation 405

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

See More

## Author Information

Paul A. Calter is a Visiting Scholar at Dartmouth College and Professor Emeritus of Mathematics at Vermont Technical College. He is a book review editor of the Nexus Network Journal and has interests in both the fields of mathematics and art. He received his B.S. from Cooper Union and his M.S. from Columbia University, both in engineering, and his Masters of Fine Arts Degree from Norwich University. Calter has taught mathematics for over twenty-five years and is the author of ten mathematics textbooks and a mystery novel. He has been an active painter and sculptor since 1968, has had many solo shows and participated in dozens of group art shows, and has permanent outdoor sculptures at a number of locations. Calter developed a course called "Geometry in Art & Architecture," which he has taught at Dartmouth College and Vermont Technical College, and he has taught at Dartmouth College and Vermont Technical College, and he has given workshops and lectures on the subject. Calter's own art is concerned with astronomical and geometric themes; he searches for a link between the organic and geometric basis of beauty, what has been called the philosopher's stone of aesthetics.
See More

## New To This Edition

· This edition contains a new chapter on statistics as well as a new section on straight line graphing.

·  Many of the exercises have been revised to ensure they are scaffolded in difficulty level from easy to challenging.

See More

Clarity of presentation:  This is the feature most mentioned by reviewers, and has obvious benefits to students and instructors.

Technical Applications:  The technical applications provide motivation for the student, and examples for an instructor who may not have a technical background. Additionally, an Index to Applications aids in finding applications in a particular field, such as electrical technology.

Estimation:  Shows a student whether an answer is reasonable or not reasonable.  They show common pitfalls for both student and instructor and are flagged and boxed, wherever appropriate.

Formulas used in the text are boxed and numbered, and listed in the Appendix as the Summary of Facts and Formulas.

Writing, Projects, Internet:  Every chapter concludes with a section of optional enrichment activities.  Many students are attracted to the magic and history of mathematics and welcome a guided introduction into this world.  These writing questions aim to test and expand a student's knowledge of the material and perhaps explore areas outside of those covered in class while team projects foster "collaborative learning."
See More
Instructors Resources
Wiley Instructor Companion Site
Technical Mathematics with Calculus, sixth Edition Annotated Instructor's Edition
ISBN: 978-0-470-53495-3 This edition provides answers next to or near problems, Teaching Tips that are helpful for instructors that are new to the course, and Applications where a topic is introduced, if the instructor does not wish to wait for those that follow later in the chapter.
Test Bank to accompany Technical Mathematics, Fifth Edition and Technical Mathematics with Calculus, Fifth Edition
This Printed Test Bank includes a collection of open response, multiple-choice, true/false, and free-response questions.
Computerized Test Bank to accompany Technical Mathematics with Calculus Sixth Edition
This Computerized Test Bank includes a collection of open response, multiple-choice, true/false, and free-response questions.
Request a print evaluation copy
See More
See Less
Students Resources
Available Materials
by Paul A. Calter
978-0-470-53494-6
This Student Solutions Manual contains the answers to odd-numbered problems and is meant to accompany Technical Mathematics, Sixth Edition.
See More
See Less
Purchase Options
Loose-leaf
Technical Mathematics Sixth Edition (Chs 1 - 22) Binder Ready Version
ISBN : 978-1-118-10783-6
832 pages
\$159.95

Hardcover
Technical Mathematics, 6th Edition
ISBN : 978-0-470-53492-2
832 pages