Technical Mathematics

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