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More About This Textbook
Overview
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 realworld, 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 computerassisted 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.
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Meet the Author
Calter is involved in the Mathematics Across the Curriculum movement, and has developed and taught a course called Geometry in Art and Architecture at Dartmouth College under an NSF grant.
Professor Calter is the author of several other mathematics textbooks, among which are the Schaum's Outline of Technical Mathematics, Problem Solving with Computers, Practical Math Handbook for the Building Trades, Practical Math for Electricity and Electronics, Mathematics for Computer Technology, Introductory Algebra and Trigonometry, Technical Calculus, and Squaring the Circle: Geometry in Art and Architecture.
Michael Calter is Associate Professor at Wesleyan University. He received his B.S. from the University of Vermont. After receiving his Ph.D. from Harvard University, he completed a postdoctoral fellowship at the University of California at Irvine. Michael has been working on his father's mathematics texts since 1983, when he completed a set of programs to accompany Technical Mathematics with Calculus. Since that time, he has become progressively more involved with his father's writing endeavors, culminating with becoming coauthor on the second edition of Technical Calculus and the fourth edition of Technical Mathematics with Calculus. Michael also enjoys the applications of mathematical techniques to chemical and physical problems as part of his academic research. Michael is a member of the American Mathematical Association of Two Year Colleges, the American Association for the Advancement of Science, and the American Chemical Society.
Michael and Paul enjoy hiking and camping trips together. These have included an expedition up Mt. Washington in January, a hike across Vermont, a walk across England on Hadrian's Wall, and many sketching trips into the mountains.
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 NonPerpendicular 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 SecondOrder Determinants 302
10–4 HigherOrder 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 HalfAngles 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 A0
B Conversion Factors A0
C Table of Integrals A0
Indexes
Applications Index I0
Index to Writing Questions I0
Index to Projects I0
General Index I0