Basic Engineering Mathematics

John Bird BSc (Hons) CEng CMath CSci FIET MIEE FIIE FIMA FCollT0750665750, 9780750665759, 9781423724117

Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically for the needs of engineers. The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult. All students taking vocational engineering courses who require fundamental knowledge of mathematics for engineering and do not have prior knowledge beyond basic school mathematics, will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering and Intermediate GNVQ, and is matched to BTEC First specifications. However Level 3 students will also find this text to be a useful resource for getting to grips with the essential mathematics concepts needed for their study, as the compulsory topics required in BTEC National and AVCE / A Level courses are also addressed. The fourth edition incorporates new material on adding waveforms, graphs with logarithmic scales, and inequalities – key topics needed for GCSE and Level 2 study. John Bird ‘s approach is based on numerous worked examples, supported by 600 worked problems, followed by 1050 further problems within exercises included throughout the text. In addition, 15 Assignments are included at regular intervals. Ideal for use as tests or homework, full solutions to the Assignments are supplied in the accompanying Instructor’s Manual, available as a free download for lecturers from http://textbooks.elsevier.com. * Unique in introducing fundamental mathematics from an engineering perspective, with a starting point below GCSE level * Fully matched to BTEC First and BTEC National core unit specifications * Free instructor’s manual available to download – contains worked solutions and suggested mark scheme

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Table of contents :
Cover……Page 1
Basic Engineering Mathematics……Page 4
Contents……Page 6
Preface……Page 12
1.1 Arithmetic operations……Page 14
1.2 Highest common factors and lowest common multiples……Page 16
1.3 Order of precedence and brackets……Page 17
2.1 Fractions……Page 19
2.2 Ratio and proportion……Page 21
2.3 Decimals……Page 22
2.4 Percentages……Page 24
Assignment 1……Page 26
3.2 Worked problems on indices……Page 27
3.3 Further worked problems on indices……Page 29
3.4 Standard form……Page 30
3.5 Worked problems on standard form……Page 31
3.7 Engineering notation and common prefixes……Page 32
4.1 Errors and approximations……Page 34
4.2 Use of calculator……Page 35
4.3 Conversion tables and charts……Page 38
4.4 Evaluation of formulae……Page 40
Assignment 2……Page 42
5.2 Conversion of binary to denary……Page 43
5.3 Conversion of denary to binary……Page 44
5.4 Conversion of denary to binary via octal……Page 45
5.5 Hexadecimal numbers……Page 46
6.1 Basic operations……Page 50
6.2 Laws of indices……Page 52
6.3 Brackets and factorization……Page 54
6.4 Fundamental laws and precedence……Page 56
6.5 Direct and inverse proportionality……Page 58
Assignment 3……Page 59
7.2 Worked problems on simple equations……Page 60
7.3 Further worked problems on simple equations……Page 62
7.4 Practical problems involving simple equations……Page 63
7.5 Further practical problems involving simple equations……Page 65
8.2 Worked problems on transposition of formulae……Page 67
8.3 Further worked problems on transposition of formulae……Page 68
8.4 Harder worked problems on transposition of formulae……Page 70
Assignment 4……Page 72
9.2 Worked problems on simultaneous equations in two unknowns……Page 73
9.3 Further worked problems on simultaneous equations……Page 75
9.4 More difficult worked problems on simultaneous equations……Page 76
9.5 Practical problems involving simultaneous equations……Page 78
10.2 Solution of quadratic equations by factorization……Page 82
10.3 Solution of quadratic equations by ‘completing the square’……Page 84
10.4 Solution of quadratic equations by formula……Page 85
10.5 Practical problems involving quadratic equations……Page 86
10.6 The solution of linear and quadratic equations simultaneously……Page 88
11.2 Simple inequalities……Page 90
11.3 Inequalities involving a modulus……Page 91
11.5 Inequalities involving square functions……Page 92
11.6 Quadratic inequalities……Page 93
Assignment 5……Page 95
12.2 The straight line graph……Page 96
12.3 Practical problems involving straight line graphs……Page 101
13.1 Graphical solution of simultaneous equations……Page 107
13.2 Graphical solutions of quadratic equations……Page 108
13.3 Graphical solution of linear and quadratic equations simultaneously……Page 112
13.4 Graphical solution of cubic equations……Page 113
Assignment 6……Page 115
14.2 Laws of logarithms……Page 116
14.3 Indicial equations……Page 118
14.4 Graphs of logarithmic functions……Page 119
15.2 Evaluating exponential functions……Page 120
15.3 The power series for e[sup(x)]……Page 121
15.4 Graphs of exponential functions……Page 123
15.6 Evaluating Napierian logarithms……Page 124
15.7 Laws of growth and decay……Page 126
Assignment 7……Page 129
16.1 Determination of law……Page 130
16.2 Determination of law involving logarithms……Page 132
17.2 Graphs of the form y=ax[sup(n)]……Page 137
17.3 Graphs of the form y=ab[sup(x)]……Page 140
17.4 Graphs of the form y=ae[sup(kx)]……Page 141
18.1 Angular measurement……Page 144
18.2 Types and properties of angles……Page 145
18.3 Properties of triangles……Page 147
18.4 Congruent triangles……Page 149
18.5 Similar triangles……Page 150
18.6 Construction of triangles……Page 152
Assignment 8……Page 154
19.2 The theorem of Pythagoras……Page 155
19.3 Trigonometric ratios of acute angles……Page 156
19.4 Solution of right-angled triangles……Page 158
19.5 Angles of elevation and depression……Page 160
19.6 Evaluating trigonometric ratios of any angles……Page 161
20.1 Graphs of trigonometric functions……Page 164
20.2 Angles of any magnitude……Page 165
20.3 The production of a sine and cosine wave……Page 167
20.4 Sine and cosine curves……Page 168
20.5 Sinusoidal form A sin(ωt ± a)……Page 171
Assignment 9……Page 174
21.2 Changing from Cartesian into polar co-ordinates……Page 175
21.3 Changing from polar into Cartesian co-ordinates……Page 176
21.4 Use of R → P and P → R functions on calculators……Page 177
22.2 Properties of quadrilaterals……Page 179
22.3 Worked problems on areas of plane figures……Page 180
22.4 Further worked problems on areas of plane figures……Page 184
22.5 Areas of similar shapes……Page 185
Assignment 10……Page 186
23.2 Properties of circles……Page 187
23.3 Arc length and area of a sector……Page 188
23.4 The equation of a circle……Page 191
24.2 Worked problems on volumes and surface areas of regular solids……Page 193
24.3 Further worked problems on volumes and surface areas of regular solids……Page 195
24.4 Volumes and surface areas of frusta of pyramids and cones……Page 199
24.5 Volumes of similar shapes……Page 202
Assignment 11……Page 203
25.1 Areas of irregular figures……Page 204
25.2 Volumes of irregular solids……Page 206
25.3 The mean or average value of a waveform……Page 207
26.3 Worked problems on the solution of triangles and their areas……Page 211
26.4 Further worked problems on the solution of triangles and their areas……Page 213
26.5 Practical situations involving trigonometry……Page 214
26.6 Further practical situations involving trigonometry……Page 217
Assignment 12……Page 219
27.2 Vector addition……Page 220
27.3 Resolution of vectors……Page 222
27.4 Vector subtraction……Page 223
27.5 Relative velocity……Page 225
28.2 Plotting periodic functions……Page 227
28.3 Determining resultant phasors by calculation……Page 228
29.2 The n’th term of a series……Page 231
29.3 Arithmetic progressions……Page 232
29.4 Worked problems on arithmetic progression……Page 233
29.5 Further worked problems on arithmetic progressions……Page 234
29.6 Geometric progressions……Page 235
29.7 Worked problems on geometric progressions……Page 236
29.8 Further worked problems on geometric progressions……Page 237
Assignment 13……Page 238
30.1 Some statistical terminology……Page 239
30.2 Presentation of ungrouped data……Page 240
30.3 Presentation of grouped data……Page 243
31.2 Mean, median and mode for discrete data……Page 248
31.3 Mean, median and mode for grouped data……Page 249
31.4 Standard deviation……Page 250
31.5 Quartiles, deciles and percentiles……Page 252
32.2 Laws of probability……Page 254
32.3 Worked problems on probability……Page 255
32.4 Further worked problems on probability……Page 256
Assignment 14……Page 259
33.2 Functional notation……Page 260
33.3 The gradient of a curve……Page 261
33.4 Differentiation from first principles……Page 262
33.5 Differentiation of y=ax[sup(n)] by the general rule……Page 263
33.6 Differentiation of sine and cosine functions……Page 265
33.7 Differentiation of e[sup(ax)] and ln ax……Page 266
33.8 Summary of standard derivatives……Page 267
33.10 Rates of change……Page 268
34.3 Standard integrals……Page 270
34.4 Definite integrals……Page 273
34.5 Area under a curve……Page 274
Assignment 15……Page 278
List of formulae……Page 279
Answers to exercises……Page 283
D……Page 298
I……Page 299
Q……Page 300
Y……Page 301