basic_engineering_mathematics0

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Index Abscissa, 83 Acute angle, 132, 143 Acute angled triangle, 134 Adding waveforms, 214 Addition of two periodic functions, 214 Algebra, 37 Algebraic expression, 37, 38, 41, 47 Alternate angles, 132, 147 Ambiguous case, 200 Amplitude, 156, 158 Angle, 131 Angle: lagging and leading, 157 types and properties of, 132 Angles of: any magnitude, 152 depression, 147 elevation, 147 Angular measurement, 131 Angular velocity, 158 Annulus, 169 Approximate value of calculations, 21, 22 Arbitrary constant of integration, 257 Arc, 174 Arc length, 175 Area under a curve, 261 Areas: irregular figures, 191, 263 plane figures, 166 sector, 167, 175 similar shapes, 172 triangles, 21, 167, 198 Arithmetic, <strong>basic</strong>, 1–4 Arithmetic progressions, 219 Average, 235 Average value of waveform, 194 Bar charts, 227 Bases, 14, 30 Binary numbers, 30–33 Blunder, 21, 22 BODMAS, 4, 7, 43 Boyle’s law, 45, 46 Brackets, 4, 41–43 Calculation of resultant phasors, 215–217 Calculations, 21–24 Calculator, 22–24, 103, 107, 111, 148, 164 Calculus, 247 Cancelling, 6, 7 Cartesian axes, 83 Cartesian co-ordinates, 162 Charle’s law, 45, 46 Chord, 174 Circle, 174 equation of, 178 properties of, 174 Circumference, 174 Classes, 230 Class: interval, 230 limits, 230 mid-point, 232 Coefficient of proportionality, 45 Common difference, 219 Common logarithms, 103 Common prefixes, 19, 20 ratio, 222 Complementary angles, 132 Completing the square, 71, 80 Computer numbering systems, 30 Cone, 180, 186 frustum of, 186 Congruent triangles, 136 Construction of triangles, 139, 140 Continuous data, 226 Conversion tables and charts, 25 Co-ordinates, 83 Corresponding angles, 132 Cosine, 143, 145, 148 graph of, 151, 154, 155 Cosine rule, 198 Cosine wave, 154, 155 Cubic equation, 100 Cuboid, 180 Cumulative frequency distribution, 230, 233 curve, 230 Cylinder, 180 Deciles, 239 Decimal: fraction, 9 places, 9–11 system, 9 Decimals, 9 Definite integrals, 260
286 Index Degrees, 131 Denary system, 30, 33 Denominator, 6 Dependent event, 241 Dependent variable, 45 Depression, angle of, 147 Derivatives, 249 standard list, 254 Determination of law, 88, 117 involving logarithms, 119 Diameter, 174 Difference of two squares, 70 Differential calculus, 247 coefficient, 249 Differentiation, 247, 249 from first principles, 249 of ax n , 250 of e ax and ln ax, 253 of sine and cosine functions, 252 successive, 255 Digits, 9, 30 Direct proportion, 8, 45 Discrete data, 226 standard deviation, 237 Dividend, 38 Division, 1 Divisor, 38 Elevation, angle of, 147 Engineering notation, 19 Equation, 47 of circle, 178 Equations: cubic, 100 linear and quadratic, simultaneously, 75, 99 quadratic, 69, 76, 95 simple, 47 simultaneous, 60–68 Equilateral triangle, 134 Errors, 21 Evaluation of formulae, 21, 27 Expectation, 241 Exponent, 17–19 Exponential functions, 107 graphs of, 110 Expression, 47 Exterior angle of triangle, 134 Extrapolation, 89 Factorization, 41, 69, 80 Factors, 3 False axes, 89 Formula, 27, 72 Formulae: evaluation of, 21, 27 list of, 266–269 transposition of, 54–59 Fractions, 6 Frequency, 158, 226 Frequency distribution, 230, 231, 232 Frequency polygon, 230, 233 Frustum, 186 Full wave rectified waveform, 194 Functional notation, 247, 249 Geometric progressions, 222 Geometry, 131 Gradient, 83 of a curve, 248 Graphical solution of equations, 94 cubic, 100, 101 linear and quadratic, simultaneously, 75, 99 quadratic, 95–99 simultaneous, 94 Graphs, 83, 94 exponential functions, 110 logarithmic functions, 106 sine and cosine, 155 straight lines, 83 trigonometric functions, 151 with logarithmic scales, 124 of the form y = ax n , 124 of the form y = ab x , 127 of the form y = ae kx , 128 Grouped data, 230 mean, median and mode, 236 standard deviation, 238 Growth and decay, laws of, 113 Half-wave rectified waveform, 194 Heptagon, 166 Hexadecimal number, 33–36 Hexagon, 166 Highest common factor (HCF), 3 Histogram, 230, 231, 233, 236 Hooke’s law, 45 Horizontal bar chart, 227 Hyperbolic logarithms, 103, 111 Hypotenuse, 142 Identity, 47 Improper fraction, 6 Indefinite integrals, 260 Independent event, 241 Independent variable, 45 Indices, 14 laws of, 14, 39, 265 Indicial equations, 105 Inequalities, 77 involving a modulus, 78 involving quotients, 79 involving square functions, 79 quadratic, 80 simple, 77, 78 Integers, 1 Integral calculus, 247 Integrals, 257 definite, 260 standard, 257 Integration, 247, 257 of ax n , 257 Intercept, y-axis, 84, 86
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Basic Engineering Mathematics
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Basic Engineering Mathematics Fourt
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Contents Preface xi 1. Basic arithm
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Contents vii 13.3 Graphical solutio
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Contents ix 27.4 Vector subtraction
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Preface Basic Engineering Mathemati
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1 Basic arithmetic 1.1 Arithmetic o
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Basic arithmetic 3 12. −23148 −
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Basic arithmetic 5 Problem 18. 23
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Fractions, decimals and percentages
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Indices and standard form 15 From l
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Indices and standard form 17 16 2
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Indices and standard form 19 3.6 Fu
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4 Calculations and evaluation of fo
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Calculations and evaluation of form
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Computer numbering systems 31 3. (a
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Computer numbering systems 33 11 11
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Computer numbering systems 35 Probl
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6 Algebra 6.1 Basic operations Alge
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Algebra 39 ) 2a 2 − 2ab − b 2 2
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Algebra 41 Using the third and four
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Algebra 43 x 2 is a common factor o
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Algebra 45 10. p 2 − 3pq × 2p ÷
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7 Simple equations 7.1 Expressions,
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Simple equations 49 7.3 Further wor
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Simple equations 51 Problem 18. A r
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Simple equations 53 Squaring both s
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Transposition of formulae 55 Rearra
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Transposition of formulae 57 Now tr
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Transposition of formulae 59 6. 7.
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Simultaneous equations 61 Hence y =
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Simultaneous equations 63 It is oft
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Simultaneous equations 65 Thus the
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Simultaneous equations 67 Substitut
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10 Quadratic equations 10.1 Introdu
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Quadratic equations 71 In Problems
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Quadratic equations 73 Summarizing:
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Quadratic equations 75 Neglecting t
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11 Inequalities 11.1 Introduction t
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Inequalities 79 i.e. 11.4 Inequalit
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Inequalities 81 Solving quadratic i
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12 Straight line graphs 12.1 Introd
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Straight line graphs 85 Problem 2.
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Straight line graphs 87 (b) Rearran
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Straight line graphs 89 Degrees Fah
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Straight line graphs 91 y 147 140 A
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Straight line graphs 93 Stress (pas
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Graphical solution of equations 95
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14 Logarithms 14.1 Introduction to
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Logarithms 105 i.e. −5 = 4x i.e.
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15 Exponential functions 15.1 The e
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Exponential functions 109 If in the
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Exponential functions 111 Problem 1
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Exponential functions 113 ( ) 5.14
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Exponential functions 115 (b) Trans
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16 Reduction of non-linear laws to
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Reduction of non-linear laws to lin
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Graphs with logarithmic scales 125
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18 Geometry and triangles 18.1 Angu
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Geometry and triangles 133 (d) 227
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Geometry and triangles 135 (a) Equi
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Geometry and triangles 137 Hence XZ
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Geometry and triangles 139 Now try
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Geometry and triangles 141 Assignme
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Introduction to trigonometry 143 Fr
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Introduction to trigonometry 145 Si
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Introduction to trigonometry 147 If
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Introduction to trigonometry 149 To
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20 Trigonometric waveforms 20.1 Gra
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Trigonometric waveforms 153 between
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Trigonometric waveforms 155 45° 60
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Trigonometric waveforms 157 y 4 0 y
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Trigonometric waveforms 159 v rads/
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Trigonometric waveforms 161 Assignm
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Cartesian and polar co-ordinates 16
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Cartesian and polar co-ordinates 16
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Areas of plane figures 167 W X Tabl
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Areas of plane figures 169 (b) Area
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Areas of plane figures 171 14. Calc
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Areas of plane figures 173 is 12 50
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The circle 175 Q B Now try the foll
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The circle 177 From equation (2), a
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The circle 179 Thus, for example, t
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Volumes of common solids 181 Proble
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Volumes of common solids 183 Proble
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Volumes of common solids 185 Fig. 2
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Volumes of common solids 187 From F
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Volumes of common solids 189 Volume
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25 Irregular areas and volumes and
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Irregular areas and volumes and mea
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Triangles and some practical applic
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27 Vectors 27.1 Introduction Some p
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Vectors 209 r 10° b Having obtaine
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Vectors 211 b Fig. 27.11 o Fig. 27.
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Vectors 213 N Thus the velocity of
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Adding of waveforms 215 y 6.1 6 4 2
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Adding of waveforms 217 The horizon
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Number sequences 219 The first four
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Number sequences 221 5. Determine t
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Number sequences 223 Hence 1 ( 1 9
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Number sequences 225 Now try the fo
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Presentation of statistical data 22
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Page 248 and 249: 31 Measures of central tendency and
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Page 254 and 255: 32 Probability 32.1 Introduction to
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Page 258 and 259: Probability 245 Two brass washers a
Page 260 and 261: 33 Introduction to differentiation
Page 262 and 263: Introduction to differentiation 249
Page 270 and 271: 34 Introduction to integration 34.1
Page 272 and 273: Introduction to integration 259 ∫
Page 274 and 275: Introduction to integration 261 Pro
Page 276 and 277: Introduction to integration 263 A t
Page 278 and 279: Introduction to integration 265 Ass
Page 280 and 281: List of formulae 267 (ii) Parallelo
Page 282 and 283: List of formulae 269 Cartesian and
Page 284 and 285: Answers to exercises 271 Exercise 7
Page 286 and 287: Answers to exercises 273 7. ab 6 c
Page 288 and 289: Answers to exercises 275 5. 0.013 3
Page 300 and 301: Index 287 Interior angles, 132, 134
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