Fundamentals of Engineering Mathematics – ICE Textbooks

Contents About the authors ix
About the editors xi
Preface xiii
1 Algebra 1
1.1 Introduction 1
1.2 Fundamental arithmetic operations and rules 1
1.3 Fractions 2
1.4 Exponents and the laws of exponents (or indices) 2
1.5 Powers of ten and their use in scientific notation 3
1.6 Radicals and laws of radicals 4
1.7 Logarithm (log) and logarithm rules 4
1.8 Progressions 5
1.9 Factorials 8
1.10 Permutations and combinations 9
1.11 Binomial and binomial theorem 11
1.12 Useful expansions for engineering applications 13
1.13 Polynomials 14
1.14 Theorem of joint variation 16
Chapter summary 16
Questions for practice 17
Reference 18
Further reading 18
2 Trigonometry 19
2.1 Introduction 19
2.2 Measurement of angles 19
2.3 Right-angled triangles and Pythagoras’ theorem 20
2.4 Trigonometric functions or ratios 21
2.5 Properties of triangles: sine and cosine rules 24
Chapter summary 26
Questions for practice 26
Further reading 27
3 Plane and coordinate geometry 29
3.1 Introduction 29
3.2 Cartesian and polar coordinate systems 29
3.3 Fundamental formulae 31
3.4 Proportional triangles 31
3.5 Equations for a straight line 31
3.6 The circle 33
3.7 The parabola 33
3.8 The ellipse 34
3.9 The hyperbola 34
Chapter summary 36
Questions for practice 36
Further reading 37
4 Calculus 39
4.1 Introduction 39
4.2 Limits 39
4.3 Applications of calculus 44
4.4 Forming differential equations 47
Chapter summary 52
Questions for practice 52
Further reading 53
5 Probability and statistics 55
5.1 Introduction 55
5.2 Statistical terminology 55
5.3 Descriptive statistics essentials 56
5.4 Graphical presentation 60
5.5 Probability 66
Chapter summary 75
Questions for practice 76
Further reading 77
6 Properties of area 79
6.1 Introduction 79
6.2 Area integral 80
6.3 Mass integral 81
6.4 Some standard results 96
6.5 Further applications of first and second moments of area 102
Chapter summary 104
Questions for practice 105
Further reading 105
7 Equilibrium of bodies 107
7.1 Introduction 107
7.2 Structural actions 107
7.3 Stability of rigid bodies 115
Chapter summary 125
Questions for practice 125
Further reading 127
8 Dimensional analysis 129
8.1 Introduction 129
8.2 Physical quantities and units of measurement 129
8.3 Unit conversion 134
8.4 Dimensional analysis 136
Chapter summary 149
Questions for practice 149
References 150
Further reading 151
9 Experimental data analysis 153
9.1 Introduction 153
9.2 Experimental errors 154
9.3 Random errors 154
9.4 Systematic errors 155
9.5 The mean: a point estimate 156
9.6 The standard error of the mean 156
9.7 An interval estimate of a measurement 156
9.8 Modelling quantisation errors 158
9.9 Combining errors 158
9.10 Hypothesis testing: the significance of the difference sample
and population means 160
9.11 Hypothesis testing: the significance of the difference between
two experiments 161
9.12 Fitting a function to data 162
9.13 Using Excel for regression analysis 162
9.14 The significance of r 167
Chapter summary 168
Further reading 168
Appendix: Frequently used units and symbols in mathematics
and mechanics 169
Index 173