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
Author(s): John Bird BSc (Hons) CEng CMath CSci FIET MIEE FIIE FIMA FCollT
Edition: 4
Publisher: Newnes
Year: 2005
Language: English
Pages: 300
Cover......Page 1
Basic Engineering Mathematics......Page 4
Contents......Page 6
Preface......Page 12
1.1 Arithmetic operations......Page 13
1.2 Highest common factors and lowest common multiples......Page 15
1.3 Order of precedence and brackets......Page 16
2.1 Fractions......Page 18
2.2 Ratio and proportion......Page 20
2.3 Decimals......Page 21
2.4 Percentages......Page 23
Assignment 1......Page 25
3.2 Worked problems on indices......Page 26
3.3 Further worked problems on indices......Page 28
3.4 Standard form......Page 29
3.5 Worked problems on standard form......Page 30
3.7 Engineering notation and common prefixes......Page 31
4.1 Errors and approximations......Page 33
4.2 Use of calculator......Page 34
4.3 Conversion tables and charts......Page 37
4.4 Evaluation of formulae......Page 39
Assignment 2......Page 41
5.2 Conversion of binary to denary......Page 42
5.3 Conversion of denary to binary......Page 43
5.4 Conversion of denary to binary via octal......Page 44
5.5 Hexadecimal numbers......Page 45
6.1 Basic operations......Page 49
6.2 Laws of indices......Page 51
6.3 Brackets and factorization......Page 53
6.4 Fundamental laws and precedence......Page 55
6.5 Direct and inverse proportionality......Page 57
Assignment 3......Page 58
7.2 Worked problems on simple equations......Page 59
7.3 Further worked problems on simple equations......Page 61
7.4 Practical problems involving simple equations......Page 62
7.5 Further practical problems involving simple equations......Page 64
8.2 Worked problems on transposition of formulae......Page 66
8.3 Further worked problems on transposition of formulae......Page 67
8.4 Harder worked problems on transposition of formulae......Page 69
Assignment 4......Page 71
9.2 Worked problems on simultaneous equations in two unknowns......Page 72
9.3 Further worked problems on simultaneous equations......Page 74
9.4 More difficult worked problems on simultaneous equations......Page 75
9.5 Practical problems involving simultaneous equations......Page 77
10.2 Solution of quadratic equations by factorization......Page 81
10.3 Solution of quadratic equations by ‘completing the square’......Page 83
10.4 Solution of quadratic equations by formula......Page 84
10.5 Practical problems involving quadratic equations......Page 85
10.6 The solution of linear and quadratic equations simultaneously......Page 87
11.2 Simple inequalities......Page 89
11.3 Inequalities involving a modulus......Page 90
11.5 Inequalities involving square functions......Page 91
11.6 Quadratic inequalities......Page 92
Assignment 5......Page 94
12.2 The straight line graph......Page 95
12.3 Practical problems involving straight line graphs......Page 100
13.1 Graphical solution of simultaneous equations......Page 106
13.2 Graphical solutions of quadratic equations......Page 107
13.3 Graphical solution of linear and quadratic equations simultaneously......Page 111
13.4 Graphical solution of cubic equations......Page 112
Assignment 6......Page 114
14.2 Laws of logarithms......Page 115
14.3 Indicial equations......Page 117
14.4 Graphs of logarithmic functions......Page 118
15.2 Evaluating exponential functions......Page 119
15.3 The power series for e[sup(x)]......Page 120
15.4 Graphs of exponential functions......Page 122
15.6 Evaluating Napierian logarithms......Page 123
15.7 Laws of growth and decay......Page 125
Assignment 7......Page 128
16.1 Determination of law......Page 129
16.2 Determination of law involving logarithms......Page 131
17.2 Graphs of the form y=ax[sup(n)]......Page 136
17.3 Graphs of the form y=ab[sup(x)]......Page 139
17.4 Graphs of the form y=ae[sup(kx)]......Page 140
18.1 Angular measurement......Page 143
18.2 Types and properties of angles......Page 144
18.3 Properties of triangles......Page 146
18.4 Congruent triangles......Page 148
18.5 Similar triangles......Page 149
18.6 Construction of triangles......Page 151
Assignment 8......Page 153
19.2 The theorem of Pythagoras......Page 154
19.3 Trigonometric ratios of acute angles......Page 155
19.4 Solution of right-angled triangles......Page 157
19.5 Angles of elevation and depression......Page 159
19.6 Evaluating trigonometric ratios of any angles......Page 160
20.1 Graphs of trigonometric functions......Page 163
20.2 Angles of any magnitude......Page 164
20.3 The production of a sine and cosine wave......Page 166
20.4 Sine and cosine curves......Page 167
20.5 Sinusoidal form A sin(ωt ± a)......Page 170
Assignment 9......Page 173
21.2 Changing from Cartesian into polar co-ordinates......Page 174
21.3 Changing from polar into Cartesian co-ordinates......Page 175
21.4 Use of R → P and P → R functions on calculators......Page 176
22.2 Properties of quadrilaterals......Page 178
22.3 Worked problems on areas of plane figures......Page 179
22.4 Further worked problems on areas of plane figures......Page 183
22.5 Areas of similar shapes......Page 184
Assignment 10......Page 185
23.2 Properties of circles......Page 186
23.3 Arc length and area of a sector......Page 187
23.4 The equation of a circle......Page 190
24.2 Worked problems on volumes and surface areas of regular solids......Page 192
24.3 Further worked problems on volumes and surface areas of regular solids......Page 194
24.4 Volumes and surface areas of frusta of pyramids and cones......Page 198
24.5 Volumes of similar shapes......Page 201
Assignment 11......Page 202
25.1 Areas of irregular figures......Page 203
25.2 Volumes of irregular solids......Page 205
25.3 The mean or average value of a waveform......Page 206
26.3 Worked problems on the solution of triangles and their areas......Page 210
26.4 Further worked problems on the solution of triangles and their areas......Page 212
26.5 Practical situations involving trigonometry......Page 213
26.6 Further practical situations involving trigonometry......Page 216
Assignment 12......Page 218
27.2 Vector addition......Page 219
27.3 Resolution of vectors......Page 221
27.4 Vector subtraction......Page 222
27.5 Relative velocity......Page 224
28.2 Plotting periodic functions......Page 226
28.3 Determining resultant phasors by calculation......Page 227
29.2 The n’th term of a series......Page 230
29.3 Arithmetic progressions......Page 231
29.4 Worked problems on arithmetic progression......Page 232
29.5 Further worked problems on arithmetic progressions......Page 233
29.6 Geometric progressions......Page 234
29.7 Worked problems on geometric progressions......Page 235
29.8 Further worked problems on geometric progressions......Page 236
Assignment 13......Page 237
30.1 Some statistical terminology......Page 238
30.2 Presentation of ungrouped data......Page 239
30.3 Presentation of grouped data......Page 242
31.2 Mean, median and mode for discrete data......Page 247
31.3 Mean, median and mode for grouped data......Page 248
31.4 Standard deviation......Page 249
31.5 Quartiles, deciles and percentiles......Page 251
32.2 Laws of probability......Page 253
32.3 Worked problems on probability......Page 254
32.4 Further worked problems on probability......Page 255
Assignment 14......Page 258
33.2 Functional notation......Page 259
33.3 The gradient of a curve......Page 260
33.4 Differentiation from first principles......Page 261
33.5 Differentiation of y=ax[sup(n)] by the general rule......Page 262
33.6 Differentiation of sine and cosine functions......Page 264
33.7 Differentiation of e[sup(ax)] and ln ax......Page 265
33.8 Summary of standard derivatives......Page 266
33.10 Rates of change......Page 267
34.3 Standard integrals......Page 269
34.4 Definite integrals......Page 272
34.5 Area under a curve......Page 273
Assignment 15......Page 277
List of formulae......Page 278
Answers to exercises......Page 282
D......Page 297
I......Page 298
Q......Page 299
Y......Page 300
