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From Counting to Addition 7 Figure 1-6 Ten rows of 10 items in each layer is a hundred (100). Ten layers of 100 is a thousand (1000). We can build up large numbers such as 2563 in this way.
8 Mastering Technical Mathematics Figure 1-7 Using rows, columns and layers to represent numbers that contain zeros. At A, there are 3065 items; at B, there are 4370 items; at C, there are 2504 items; at D, there are 3008 items. MILLIONS AND MORE Imagine stacking thousands of “boxes” to get a powerful way of counting. In Fig. 1-8, one complete box that contains 1000 apples is magnified in a “stack” that has 999 other identical boxes. Think about it: 1000 boxes, each with 1000 apples in it! Each layer of 10 by 10 boxes contains a hundred thousand (100,000) apples. Each row or column of ten boxes in a layer contains ten thousand (10,000) apples. The whole stack contains a thousand thousand or a million (1,000,000) apples. You can go on with this. Suppose each of the tiniest boxes in the magnifying glass is really a stack containing 1,000,000? Then the 10-by-10-by-10 “superbox” in the glass has a thousand million (1,000,000,000) apples. In the United States this is called a billion. The entire stack in this case has a million million (1,000,000,000,000) apples. In the United States it is called a trillion, but some people in England call it a billion. If you go to another multiple of a thousand, you get a quadrillion (written as a one with fifteen
Page 2 and 3: Mastering Technical Mathematics
Page 4 and 5: Mastering Technical Mathematics Thi
Page 6 and 7: To Tim, Samuel, and Tony
Page 8 and 9: For more information about this tit
Page 10 and 11: Contents ix Real Vs. Imaginary Numb
Page 12 and 13: Contents xi Navigator’s Polar Vs.
Page 14 and 15: Contents xiii Law of Large Numbers
Page 16 and 17: Introduction This book is intended
Page 18 and 19: Copyright © 2008, 1999 by The McGr
Page 20 and 21: 1From Counting to Addition We’ve
Page 22 and 23: From Counting to Addition 5 Figure
Page 30 and 31: From Counting to Addition 13 WEIGHT
Page 34 and 35: 13. In the United States, common li
Page 36 and 37: 2Subtraction Just as addition is co
Page 38 and 39: Subtraction 21 the hundreds column,
Page 40 and 41: Subtraction 23 MAKING CHANGE This i
Page 42 and 43: Subtraction 25 Figure 2-6 Two metho
Page 44 and 45: 3Multiplication Suppose you go into
Page 46 and 47: Multiplication 29 In Fig. 3-2A, exa
Page 48 and 49: Multiplication 31 Figure 3-3 An exa
Page 50 and 51: Multiplication 33 Figure 3-6 It doe
Page 52 and 53: Multiplication 35 Figure 3-9 Subtra
Page 54 and 55: Multiplication 37 Figure 3-12 Multi
Page 56 and 57: Multiplication 39 3. Multiply the f
Page 58 and 59: 4Division Before the days of electr
Page 60 and 61: Division 43 Figure 4-2 A pictorial
Page 62 and 63: Division 45 MULTIPLICATION CHECKS D
Page 64 and 65: Division 47 Figure 4-6 At A, we can
Page 66 and 67: Division 49 In the example of Fig.
Page 68 and 69: Division 51 7/10 0.7 17/20 0.85 3
Page 70 and 71: Division 53 QUESTIONS AND PROBLEMS
Page 72 and 73: 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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If the mass is 1 kg, the force is 9
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13 Ratio and Proportion Thus far, t
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Ratio and Proportion 175 PROPORTION
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In any triangle, its three interior
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Ratio and Proportion 179 Figure 13-
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14 Trigonometric and Geometric Calc
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Trigonometric and Geometric Calcula
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PROPERTIES OF THE ISOSCELES TRIANGL
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Suppose you name the equal pairs of
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Copyright © 2008, 1999 by The McGr
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15 Systems of Counting The decimal
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Systems of Counting 205 Figure 15-2
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Systems of Counting 207 OCTAL NUMBE
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Systems of Counting 209 DECIMAL BIN
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are shortcut methods for performing
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1. Find the decimal equivalent of t
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16 Progressions, Permutations, and
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Progressions, Permutations, and Com
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17 Introduction to Derivatives The
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Figure 17-2 The derivative of the f
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is negative when x is negative, bec
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This rule holds true for all expres
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Introduction to Derivatives 243 CIR
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Introduction to Derivatives 245 Fig
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18 More about Differentiation The p
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More about Differentiation 253 Figu
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More about Differentiation 255 by t
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More about Differentiation 257 MULT
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In the powers table, 0 n is always
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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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