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Index 287 Interior angles, 132, 134 Interpolation, 89 Inverse proportion, 8, 45 Irregular areas, 191 Irregular volumes, 191, 192 Isosceles triangle, 134 Lagging angle, 157, 158 Laws of: algebra, 37 growth and decay, 113 indices, 14, 39 logarithms, 103 precedence, 4, 43 probability, 241 Leading angle, 157, 158 Leibniz notation, 249 Limiting value, 248 Linear and quadratic equations simultaneously, 99 Logarithmic functions, graphs of, 106 Logarithmic scales, 124 Logarithms, 103 laws of, 103 Log–linear graph paper, 127–129 Log–log graph paper, 124 Long division, 2, 10 Lower class boundary, 230 Lowest common multiple (LCM), 3, 49 Major arc, 174 Major sector, 174 Major segment, 174 Mantissa, 17 Maximum value, 95 Mean, 235 value of waveform, 191, 194 Measures of central tendency, 235 Median, 235, 238 Member of set, 226 Mensuration, 166 Mid-ordinate rule, 191, 264 Minimum value, 95 Minor arc, 174 Minor sector, 174 Minor segment, 174 Mixed number, 6 Mode, 235 Modulus, 78 Multiple, 3 Napierian logarithms, 103, 111 Natural logarithms, 103, 111 Nose-to-tail method, 208 Number sequences, 218 Numerator, 6 Obtuse angle, 132, 134 Obtuse angled triangle, 134 Octagon, 166, 171 Octal numbers, 32–34 Ogive, 230, 233, 239 Ohm’s law, 45 Order of magnitude error, 21, 22 Order of precedence, 4, 7 Ordinate, 83 Parabola, 95 Parallel lines, 132 Parallelogram, 166 method, 208 Pentagon, 166 Percentage component bar chart, 227 Percentage relative frequency, 226 Percentages, 6, 11 Percentile, 239 Perfect square, 70–72 Perimeter, 134 Period, 156 Periodic function, 155 Periodic time, 158 Phasor, 158, 214 Pictograms, 227 Pie diagram, 227, 229 Planimeter, 191 Plotting periodic functions, 214 Polar co-ordinates, 162 Polygon, 166 frequency, 230, 233 Population, 226 Power, 14, 17 series for e x , 108, 109 Practical problems: quadratic equations, 73–75 simple equations, 50–53 simultaneous equations, 65–68 straight line graphs, 88–91 trigonometry, 201–205 Precedence, 4, 43, 44 Prefixes, 19, 20 Prism, 180 Probability, 241 laws of, 241 Progression: arithmetic, 219 geometric, 222 Properties of triangles, 134 Proper fraction, 6, 10 Proportion, 8, 45 Pyramid, 183 volumes and surface area of frustum of, 186 Pythagoras’ theorem, 56, 142, 143, 162, 198 Quadrant, 174 Quadratic equations, 69 by completing the square, 69, 71, 72 factorization, 69 formula, 69, 72 practical problems, 73–75 Quadratic formula, 72 Quadratic graphs, 95 Quadratic inequalities, 80 Quadrilaterals, 166 properties of, 166
288 Index Quartiles, 239 Quotients, inequalities involving, 79 Radians, 131, 158, 175 Radius, 174 Radix, 30 Range, 230 Ranking, 235 Rates of change, 254 Ratio and proportion, 8, 9 Reciprocal, 14 Rectangle, 166 Rectangular axes, 83, 152 co-ordinates, 164 Rectangular prism, 180 Reduction of non-linear laws to linear form, 117 Reflex angle, 132, 133 Relative frequency, 226 Relative velocity, 212 Resolution of vectors, 209 Resultant phasors, by calculation, 215 Rhombus, 166, 168 Right angle, 132 Right angled triangle, 134 solution of, 145 Rounding-off errors, 21 Sample, 226 Scalar quantities, 207 Scalene triangle, 134 Sector, 167, 174, 227 area of, 167, 175 Segment, 174 Semicircle, 167, 174 Semi-interquartile range, 239 Sequences, 218 Series, n’th term of, 218 Square numbers, 219 Set, 226, 230 Sequence of numbers, 218 Short division, 2 Significant figures, 9 Similar shapes, 172, 189 Similar triangles, 137, 138, 186 Simple equations, 47–51 practical problems, 50–53 Simple inequalities, 77, 78 Simpson’s rule, 192, 264 Simultaneous equations, 60–68, 94 practical problems, 65–68 Sine, 143, 145, 148 graph of, 151, 155 Sine rule, 198 wave, 154, 155, 194 Sinusoidal form A sin(ωt ± α), 158, 216 Slope, 83 Space diagram, 212 Sphere, 180 Square, 14, 166 root, 14, 49, 50, 56, 71 Square functions, inequalities involving, 79 Standard deviation, 237 Standard differentials, 254 integrals, 257 Standard form, 14, 17–19 Statistical data, presentation of, 226 Straight line graphs, 83 practical problems, 88–91 Subject of formulae, 27 Successive differentiation, 255 Sum to infinity of series, 222 Supplementary angles, 132 Surface areas of frusta of pyramids and cones, 186–189 of solids, 180–185 Symbols, 27 Tally diagram, 230–232 Tangent, 143, 148, 151, 174, 249, 253 Terminating decimal, 9 Term of series, 218 Transposition of formulae, 54–59 Transversal, 132 Trapezium, 166, 188 Trapezoidal rule, 191, 263 Triangle, 131, 134, 166 Triangles: area of, 21, 198 congruent, 136 construction of, 139, 140 properties of, 134 similar, 137, 138, 186 Trigonometric ratios, 143, 144 evaluation of, 148 graphs of, 151 Trigonometry, 142 practical situations, 201–205 Turning points, 95 Ungrouped data, 227 Upper class boundary, 230 Use of calculator, 22–24, 103, 107, 111, 148, 164 Vector addition, 207 Vector subtraction, 210 Vectors, 207 resolution of, 209 Vertical bar chart, 227 Vertically opposite angles, 132 Volumes of: common solids, 180 frusta of pyramids and cones, 186 irregular solids, 193 similar shapes, 189 Waveform addition, 214 y-axis intercept, 84 Young’s modulus of elasticity, 45, 90
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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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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
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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 298 and 299: Index Abscissa, 83 Acute angle, 132
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