Basic Engineering Mathematics, Fourth Edition

✍ Scribed by John Bird BSc (Hons) CEng CMath CSci FIET MIEE FIIE FIMA FCollT

• Publisher: Newnes
• Year: 2005
• Tongue: English
• Leaves: 297
• Edition: 4
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Table of Contents
......Page 3
1.1 Arithmetic operations......Page 10
1.2 Highest common factors and lowest common multiples......Page 12
1.3 Order of precedence and brackets......Page 13
2.1 Fractions......Page 15
2.2 Ratio and proportion......Page 17
2.3 Decimals......Page 18
2.4 Percentages......Page 20
Assignment 1......Page 22
3.2 Worked problems on indices......Page 23
3.3 Further worked problems on indices......Page 25
3.4 Standard form......Page 26
3.5 Worked problems on standard form......Page 27
3.7 Engineering notation and common prefixes......Page 28
4.1 Errors and approximations......Page 30
4.2 Use of calculator......Page 31
4.3 Conversion tables and charts......Page 34
4.4 Evaluation of formulae......Page 36
Assignment 2......Page 38
5.2 Conversion of binary to denary......Page 39
5.3 Conversion of denary to binary......Page 40
5.4 Conversion of denary to binary via octal......Page 41
5.5 Hexadecimal numbers......Page 42
6.1 Basic operations......Page 46
6.2 Laws of indices......Page 48
6.3 Brackets and factorization......Page 50
6.4 Fundamental laws and precedence......Page 52
6.5 Direct and inverse proportionality......Page 54
Assignment 3......Page 55
7.2 Worked problems on simple equations......Page 56
7.3 Further worked problems on simple equations......Page 58
7.4 Practical problems involving simple equations......Page 59
7.5 Further practical problems involving simple equations......Page 61
8.2 Worked problems on transposition of formulae......Page 63
8.3 Further worked problems on transposition of formulae......Page 64
8.4 Harder worked problems on transposition of formulae......Page 66
Assignment 4......Page 68
9.2 Worked problems on simultaneous equations in two unknowns......Page 69
9.3 Further worked problems on simultaneous equations......Page 71
9.4 More difficult worked problems on simultaneous equations......Page 72
9.5 Practical problems involving simultaneous equations......Page 74
10.2 Solution of quadratic equations by factorization......Page 78
10.3 Solution of quadratic equations by ‘completing the square’......Page 80
10.4 Solution of quadratic equations by formula......Page 81
10.5 Practical problems involving quadratic equations......Page 82
10.6 The solution of linear and quadratic equations simultaneously......Page 84
11.2 Simple inequalities......Page 86
11.3 Inequalities involving a modulus......Page 87
11.5 Inequalities involving square functions......Page 88
11.6 Quadratic inequalities......Page 89
Assignment 5......Page 91
12.2 The straight line graph......Page 92
12.3 Practical problems involving straight line graphs......Page 97
13.1 Graphical solution of simultaneous equations......Page 103
13.2 Graphical solutions of quadratic equations......Page 104
13.3 Graphical solution of linear and quadratic equations simultaneously......Page 108
13.4 Graphical solution of cubic equations......Page 109
Assignment 6......Page 111
14.2 Laws of logarithms......Page 112
14.3 Indicial equations......Page 114
14.4 Graphs of logarithmic functions......Page 115
15.2 Evaluating exponential functions......Page 116
15.3 The power series for e[sup(x)]......Page 117
15.4 Graphs of exponential functions......Page 119
15.6 Evaluating Napierian logarithms......Page 120
15.7 Laws of growth and decay......Page 122
Assignment 7......Page 125
16.1 Determination of law......Page 126
16.2 Determination of law involving logarithms......Page 128
17.2 Graphs of the form y=ax[sup(n)]......Page 133
17.3 Graphs of the form y=ab[sup(x)]......Page 136
17.4 Graphs of the form y=ae[sup(kx)]......Page 137
18.1 Angular measurement......Page 140
18.2 Types and properties of angles......Page 141
18.3 Properties of triangles......Page 143
18.4 Congruent triangles......Page 145
18.5 Similar triangles......Page 146
18.6 Construction of triangles......Page 148
Assignment 8......Page 150
19.2 The theorem of Pythagoras......Page 151
19.3 Trigonometric ratios of acute angles......Page 152
19.4 Solution of right-angled triangles......Page 154
19.5 Angles of elevation and depression......Page 156
19.6 Evaluating trigonometric ratios of any angles......Page 157
20.1 Graphs of trigonometric functions......Page 160
20.2 Angles of any magnitude......Page 161
20.3 The production of a sine and cosine wave......Page 163
20.4 Sine and cosine curves......Page 164
20.5 Sinusoidal form A sin(ωt ± a)......Page 167
Assignment 9......Page 170
21.2 Changing from Cartesian into polar co-ordinates......Page 171
21.3 Changing from polar into Cartesian co-ordinates......Page 172
21.4 Use of R → P and P → R functions on calculators......Page 173
22.2 Properties of quadrilaterals......Page 175
22.3 Worked problems on areas of plane figures......Page 176
22.4 Further worked problems on areas of plane figures......Page 180
22.5 Areas of similar shapes......Page 181
Assignment 10......Page 182
23.2 Properties of circles......Page 183
23.3 Arc length and area of a sector......Page 184
23.4 The equation of a circle......Page 187
24.2 Worked problems on volumes and surface areas of regular solids......Page 189
24.3 Further worked problems on volumes and surface areas of regular solids......Page 191
24.4 Volumes and surface areas of frusta of pyramids and cones......Page 195
24.5 Volumes of similar shapes......Page 198
Assignment 11......Page 199
25.1 Areas of irregular figures......Page 200
25.2 Volumes of irregular solids......Page 202
25.3 The mean or average value of a waveform......Page 203
26.3 Worked problems on the solution of triangles and their areas......Page 207
26.4 Further worked problems on the solution of triangles and their areas......Page 209
26.5 Practical situations involving trigonometry......Page 210
26.6 Further practical situations involving trigonometry......Page 213
Assignment 12......Page 215
27.2 Vector addition......Page 216
27.3 Resolution of vectors......Page 218
27.4 Vector subtraction......Page 219
27.5 Relative velocity......Page 221
28.2 Plotting periodic functions......Page 223
28.3 Determining resultant phasors by calculation......Page 224
29.2 The n’th term of a series......Page 227
29.3 Arithmetic progressions......Page 228
29.4 Worked problems on arithmetic progression......Page 229
29.5 Further worked problems on arithmetic progressions......Page 230
29.6 Geometric progressions......Page 231
29.7 Worked problems on geometric progressions......Page 232
29.8 Further worked problems on geometric progressions......Page 233
Assignment 13......Page 234
30.1 Some statistical terminology......Page 235
30.2 Presentation of ungrouped data......Page 236
30.3 Presentation of grouped data......Page 239
31.2 Mean, median and mode for discrete data......Page 244
31.3 Mean, median and mode for grouped data......Page 245
31.4 Standard deviation......Page 246
31.5 Quartiles, deciles and percentiles......Page 248
32.2 Laws of probability......Page 250
32.3 Worked problems on probability......Page 251
32.4 Further worked problems on probability......Page 252
Assignment 14......Page 255
33.2 Functional notation......Page 256
33.3 The gradient of a curve......Page 257
33.4 Differentiation from first principles......Page 258
33.5 Differentiation of y=ax[sup(n)] by the general rule......Page 259
33.6 Differentiation of sine and cosine functions......Page 261
33.7 Differentiation of e[sup(ax)] and ln ax......Page 262
33.8 Summary of standard derivatives......Page 263
33.10 Rates of change......Page 264
34.3 Standard integrals......Page 266
34.4 Definite integrals......Page 269
34.5 Area under a curve......Page 270
Assignment 15......Page 274
List of formulae......Page 275
Answers to exercises......Page 279
D......Page 294
I......Page 295
Q......Page 296
Y......Page 297