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Systems of Counting 213 Figure 15-8 At A, an alternative binary conversion scheme. At B, conversion of decimal 4773 and 37 to binary form using this alternative method. At C, division of binary 1001010100101 (the equivalent of decimal 4773) by binary 100101 (the equivalent of decimal 37), and conversion back to decimal form for checking.
214 Mastering Technical Mathematics power of 2, which is 8. Figure 15-9A is a comparison between powers of 2 (for the binary system) and powers of 10 (for the decimal system). From this list, you can infer some rules for using indices that help you take further shortcuts in multiplication and division. First, remember that multiplication and division Figure 15-9 At A, powers of 2 and 10 for exponents ranging from 10 to 10. At B, examples of how exponents add for multiplication and subtract for division.
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Mastering Technical Mathematics
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Mastering Technical Mathematics Thi
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To Tim, Samuel, and Tony
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For more information about this tit
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Contents ix Real Vs. Imaginary Numb
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Contents xi Navigator’s Polar Vs.
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Contents xiii Law of Large Numbers
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Introduction This book is intended
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Copyright © 2008, 1999 by The McGr
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1From Counting to Addition We’ve
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From Counting to Addition 5 Figure
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From Counting to Addition 13 WEIGHT
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13. In the United States, common li
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2Subtraction Just as addition is co
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Subtraction 21 the hundreds column,
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Subtraction 23 MAKING CHANGE This i
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Subtraction 25 Figure 2-6 Two metho
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3Multiplication Suppose you go into
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Multiplication 29 In Fig. 3-2A, exa
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Multiplication 31 Figure 3-3 An exa
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Multiplication 33 Figure 3-6 It doe
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Multiplication 35 Figure 3-9 Subtra
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Multiplication 37 Figure 3-12 Multi
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Multiplication 39 3. Multiply the f
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4Division Before the days of electr
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Division 43 Figure 4-2 A pictorial
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Division 45 MULTIPLICATION CHECKS D
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Division 47 Figure 4-6 At A, we can
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Division 49 In the example of Fig.
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Division 51 7/10 0.7 17/20 0.85 3
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Division 53 QUESTIONS AND PROBLEMS
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5Fractions Chapter 4 presented some
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Fractions 57 This line of reasoning
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Fractions 59 493/23 21.xxx . . . (
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Fractions 61 The numbers in the ori
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Fractions 63 5/12 25/60 3/10 18/6
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Fractions 65 “limiting values”
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Fractions 67 QUESTIONS AND PROBLEMS
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6Plane Polygons So far, this book h
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Plane Polygons 71 WHAT IS A SQUARE?
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Plane Polygons 73 inches is not the
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Plane Polygons 75 Figure 6-7 Two wa
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Plane Polygons 77 AREA OF AN OBTUSE
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Plane Polygons 79 Figure 6-11 Some
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Plane Polygons 81 QUESTIONS AND PRO
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7Time, Percentages, and Graphs You
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Figure 7-2 A racecar driver can cal
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When a percentage expresses a chang
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Time, Percentages, and Graphs 89 Fi
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Time, Percentages, and Graphs 91 Fi
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5-mile track. Each graph gives you
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Part 2 ALGEBRA, GEOMETRY, AND TRIGO
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8First Notions in Algebra As proble
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First Notions in Algebra 99 Figure
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First Notions in Algebra 103 (a b)
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To recap, here are the rules if you
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4. Suppose x 5 and y 7. Then what
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9Some “School” Algebra In this
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Some “School” Algebra 115 DIMEN
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Some “School” Algebra 117 4 u
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Some “School” Algebra 119 20x
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Some “School” Algebra 121 Figur
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Figure 9-9 Sometimes it’s easier
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9. Adding 1 to the numerator and de
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10Quadratic Equations Simultaneous
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Quadratic Equations 129 Figure 10-3
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What about the “negative solution
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11 Some Useful Shortcuts Have you n
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Some Useful Shortcuts 143 FINDING S
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used to derive square roots to seve
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Some Useful Shortcuts 147 Figure 11
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Some Useful Shortcuts 149 Figure 11
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Some Useful Shortcuts 151 which sim
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12. In each of the following pairs
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12 Mechanical Mathematics In this c
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Mechanical Mathematics 157 Figure 1
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is at (a times t) feet per second.
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Mechanical Mathematics 161 Figure 1
Page 180 and 181: If the mass is 1 kg, the force is 9
Page 182 and 183: Mechanical Mathematics 165 Figure 1
Page 190 and 191: 13 Ratio and Proportion Thus far, t
Page 192 and 193: Ratio and Proportion 175 PROPORTION
Page 194 and 195: In any triangle, its three interior
Page 196 and 197: Ratio and Proportion 179 Figure 13-
Page 204 and 205: 14 Trigonometric and Geometric Calc
Page 206 and 207: Trigonometric and Geometric Calcula
Page 212 and 213: PROPERTIES OF THE ISOSCELES TRIANGL
Page 214 and 215: Suppose you name the equal pairs of
Page 218 and 219: Copyright © 2008, 1999 by The McGr
Page 220 and 221: 15 Systems of Counting The decimal
Page 222 and 223: Systems of Counting 205 Figure 15-2
Page 224 and 225: Systems of Counting 207 OCTAL NUMBE
Page 226 and 227: Systems of Counting 209 DECIMAL BIN
Page 228 and 229: Systems of Counting 211 Figure 15-6
Page 232 and 233: are shortcut methods for performing
Page 234 and 235: 1. Find the decimal equivalent of t
Page 236 and 237: 16 Progressions, Permutations, and
Page 238 and 239: Progressions, Permutations, and Com
Page 252 and 253: 17 Introduction to Derivatives The
Page 254 and 255: Figure 17-2 The derivative of the f
Page 256 and 257: is negative when x is negative, bec
Page 258 and 259: This rule holds true for all expres
Page 260 and 261: Introduction to Derivatives 243 CIR
Page 262 and 263: Introduction to Derivatives 245 Fig
Page 268 and 269: 18 More about Differentiation The p
Page 270 and 271: More about Differentiation 253 Figu
Page 272 and 273: More about Differentiation 255 by t
Page 274 and 275: More about Differentiation 257 MULT
Page 276 and 277: In the powers table, 0 n is always
Page 278 and 279: DERIVATIVE OF FUNCTION MULTIPLIED B
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More about Differentiation 263 QUES
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19 Introduction to Integrals Now th
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Introduction to Integrals 267 Figur
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(it subtracts from itself), so you
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Introduction to Integrals 275 VOLUM
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1. Find the derivatives of the prod
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20Combining Calculus with Other Too
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plotting nine points, but to get a
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In a situation like this, you have
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Combining Calculus with Other Tools
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These principal axes can be regarde
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e reaches 1, the ellipse “breaks
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etween the plane and the double con
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21Alternative Coordinate Systems Th
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Alternative Coordinate Systems 303
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perpendicular to the other two. The
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22Complex Numbers Long ago, humanki
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Multiplying repeatedly by i works t
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Complex Numbers 327 Figure 22-4 The
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Complex Numbers 329 When you cube i
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Complex Numbers 331 Figure 22-9 The
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Complex Numbers 333 Figure 22-11 At
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Complex Numbers 335 QUESTIONS AND P
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Part 4 TOOLS OF APPLIED MATHEMATICS
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23Trigonometry in the Real World Tr
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The absolute accuracy (in fixed uni
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Trigonometry in the Real World 343
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objects, even when they are observe
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Now find the distance PV by applyin
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7. What is the range of the aircraf
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24Logarithms and Exponentials A log
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Logarithms and Exponentials 361 Fig
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Now try an example in which neither
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Let’s put a number into this form
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Logarithms and Exponentials 369 10
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Suppose x is some real number. The
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To demonstrate this, let b e, x 2
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“Inv” key followed by a “ln
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and so on. A decrease of 1 order of
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25Scientific Notation Tutorial In s
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Another alternative multiplication
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line that covers 3 orders of magnit
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Scientific Notation Tutorial 387 (3
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Scientific Notation Tutorial 389 (5
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equality symbols. It is universally
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Sometimes, the outcome of determini
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26Vectors You’ve already seen a f
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Vectors 397 MULTIPLICATION OF A VEC
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Vectors 399 The values of the angle
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Vectors 401 If a is multiplied by a
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Vectors 403 Figure 26-5 Direction a
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Vectors 405 This formula works in a
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Vectors 407 You are told that these
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Vectors 409 4. Consider the two vec
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27Logic and Truth Tables To gain a
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are true. If any one of the compone
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antecedent is (P & C). The “impli
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Logic and Truth Tables 417 X Y X &
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Logic and Truth Tables 419 (X 1 Y)
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Logic and Truth Tables 421 The same
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classes—a certain way that multip
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Table 27-9B Derivation of truth val
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Logic and Truth Tables 427 A X Y X
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Logic and Truth Tables 429 X Y Z X
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Logic and Truth Tables 431 X Y Z X
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28Beyond Three Dimensions As you ha
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Beyond Three Dimensions 435 Figure
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a little later! It “lives” for
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Beyond Three Dimensions 441 IMPOSSI
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Beyond Three Dimensions 443 Displac
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Beyond Three Dimensions 449 NO PARA
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such as the pyramid, cube, and sphe
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2. If there are no pairs of paralle
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29A Statistics Primer Statistics is
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A Statistics Primer 457 Figure 29-2
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A Statistics Primer 459 PARAMETER A
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A Statistics Primer 463 of dice, th
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To determine µ sc , check the tabl
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A Statistics Primer 471 making it m
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30Probability Basics Probability is
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Probability Basics 475 Event 1 Even
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Probability Basics 477 As with math
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Probability Basics 479 that both co
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Probability Basics 481 The notion o
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Probability Basics 483 To calculate
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Probability Basics 485 • 30 peopl
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Probability Basics 487 The resultin
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Probability Basics 489 Because the
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Probability Basics 491 Figure 30-11
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Probability Basics 493 views are re
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Final Exam Do not refer to the text
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Final Exam 497 (a) An even number t
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Final Exam 499 X Y Z ? F F F F F F
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Final Exam 501 (c) A harmonic progr
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Final Exam 503 (c) 1.8 10 6 km (d)
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Final Exam 505 47. Suppose an item
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Final Exam 507 Figure E-6 Illustrat
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Final Exam 509 (a) p q (b) p q 1
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Final Exam 511 (d) Roots of w (e) P
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Final Exam 513 82. Which of the fol
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Final Exam 515 (b) It decreases in
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Final Exam 517 95. In the situation
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Appendix 1 Solutions to End-of-Chap
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Solutions to End-of-Chapter Questio
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Figure A-30 Illustration for soluti
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Appendix 2 Answers to Final Exam Qu
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Appendix 3 Table of Derivatives Let
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Appendix 4 Table of Indefinite Inte
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Table of Indefinite Integrals 609 f
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Suggested Additional Reading Bluman
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Index absolute accuracy, 341 error,
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cosines, law of, 347-348 counter, m
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geometry elliptic, 449 Euclidean, 4
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exponential, 369-371 frequency, 255
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esonance, in system, 168-170, 255 r
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direction angles, 402-403 direction
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