# Basic Engineering Mathematics By Jhon Bird Free eBOOK

## Basic Engineering Mathematics By Jhon Bird

Author : Jhon Bird
Publication: ELSEVIER
Edition: 4th
Total Number of Pages: 301
Size : 2.88 MB

### CONTENTS:

#### Preface xi

1. Basic arithmetic 1
1.1 Arithmetic operations 1
1.2 Highest common factors and lowest common multiples 3
1.3 Order of precedence and brackets 4
2. Fractions, decimals and percentages 6
2.1 Fractions 6
2.2 Ratio and proportion 8
2.3 Decimals 9
2.4 Percentages 11
Assignment 1 13
3. Indices, standard form and engineering notation 14
3.1 Indices 14
3.2 Worked problems on indices 14
3.3 Further worked problems on indices 16
3.4 Standard form 17
3.5 Worked problems on standard form 18
3.6 Further worked problems on standard form 19
3.7 Engineering notation and common prefixes 19
4. Calculations and evaluation of formulae 21
4.1 Errors and approximations 21
4.2 Use of calculator 22
4.3 Conversion tables and charts 25
4.4 Evaluation of formulae 27
Assignment 2 29
5. Computer numbering systems 30
5.1 Binary numbers 30
5.2 Conversion of binary to denary 30
5.3 Conversion of denary to binary 31
5.4 Conversion of denary to binary via octal 32
6. Algebra 37
6.1 Basic operations 37
6.2 Laws of indices 39
6.3 Brackets and factorization 6.4 Fundamental laws and precedence 43
6.5 Direct and inverse proportionality 45
Assignment 3 46
7. Simple equations 47
7.1 Expressions, equations and identities 47
7.2 Worked problems on simple equations 47
7.3 Further worked problems on simple equations 49
7.4 Practical problems involving simple equations 50
7.5 Further practical problems involving simple equations 52
8. Transposition of formulae 54
8.1 Introduction to transposition of formulae 54
8.2 Worked problems on transposition of formulae 54
8.3 Further worked problems on transposition of formulae 55
8.4 Harder worked problems on transposition of formulae 57
Assignment 4 59
9. Simultaneous equations 60
9.1 Introduction to simultaneous equations 60
9.2 Worked problems on simultaneous equations in two unknowns 60
9.3 Further worked problems on simultaneous equations 62
9.4 More difficult worked problems on simultaneous equations 63
9.5 Practical problems involving simultaneous equations 65
10.1 Introduction to quadratic equations 69
10.2 Solution of quadratic equations by factorization 69
10.3 Solution of quadratic equations by ‘completing the square’ 71
10.4 Solution of quadratic equations by formula 72
10.5 Practical problems involving quadratic equations 73
10.6 The solution of linear and quadratic equations simultaneously 75
11. Inequalities 77
11.1 Introduction to inequalities 77
11.2 Simple inequalities 77
11.3 Inequalities involving a modulus 78
11.4 Inequalities involving quotients 79
11.5 Inequalities involving square functions 79
Assignment 5 82
12. Straight line graphs 83
12.1 Introduction to graphs 83
12.2 The straight line graph 83
12.3 Practical problems involving straight line graphs 88
13. Graphical solution of equations 94
13.1 Graphical solution of simultaneous equations 94
13.2 Graphical solutions of quadratic equations 95
13.3 Graphical solution of linear and quadratic equations simultaneously 99
13.4 Graphical solution of cubic equations 100
Assignment 6 102
14. Logarithms 103
14.1 Introduction to logarithms 103
14.2 Laws of logarithms 103
14.3 Indicial equations 105
14.4 Graphs of logarithmic functions 106
15. Exponential functions 107
15.1 The exponential function 107
15.2 Evaluating exponential functions 107
15.3 The power series for ex 108
15.4 Graphs of exponential functions 110
15.5 Napierian logarithms 111
15.6 Evaluating Napierian logarithms 111
15.7 Laws of growth and decay 113
Assignment 7 116
16. Reduction of non-linear laws to linear-form 117
16.1 Determination of law 117
16.2 Determination of law involving logarithms 119
17. Graphs with logarithmic scales 124
17.1 Logarithmic scales 124
17.2 Graphs of the form y=axn 124
17.3 Graphs of the form y=abx 127
17.4 Graphs of the form y=aekx 128
18. Geometry and triangles 131
18.1 Angular measurement 131
18.2 Types and properties of angles 132
18.3 Properties of triangles 134
18.4 Congruent triangles 136
18.5 Similar triangles 137
18.6 Construction of triangles 139
Assignment 8 141
19. Introduction to trigonometry 142
19.1 Trigonometry 142
19.2 The theorem of Pythagoras 142
19.3 Trigonometric ratios of acute angles 143
19.4 Solution of right-angled triangles 145
19.5 Angles of elevation and depression 147
19.6 Evaluating trigonometric ratios of any angles 148
20. Trigonometric waveforms 151
20.1 Graphs of trigonometric functions 151
20.2 Angles of any magnitude 152
20.3 The production of a sine and cosine wave 154
20.4 Sine and cosine curves 155
20.5 Sinusoidal form A sin(Ï‰t }Î±) 158
Assignment 9 161
21. Cartesian and polar co-ordinates 162
21.1 Introduction 162
21.2 Changing from Cartesian into polar co-ordinates 162
21.3 Changing from polar into Cartesian co-ordinates 163
21.4 Use of RP and PR functions on calculators 164
22. Areas of plane figures 166
22.1 Mensuration 166
22.3 Worked problems on areas of plane figures 167
22.4 Further worked problems on areas of plane figures 171
22.5 Areas of similar shapes 172
Assignment 10 173
23. The circle 174
23.1 Introduction 174
23.2 Properties of circles 174
23.3 Arc length and area of a sector 175
23.4 The equation of a circle 178
24. Volumes of common solids 180
24.1 Volumes and surface areas of regular solids 180
24.2 Worked problems on volumes and surface areas of regular solids 180
24.3 Further worked problems on volumes and surface areas of regular solids 182
24.4 Volumes and surface areas of frusta of pyramids and cones 186
24.5 Volumes of similar shapes 189
Assignment 11 190
25. Irregular areas and volumes and mean values of waveforms 191
25.1 Areas of irregular figures 191
25.2 Volumes of irregular solids 193
25.3 The mean or average value of a waveform 194
26. Triangles and some practical applications 198
26.1 Sine and cosine rules 198
26.2 Area of any triangle 198
26.3 Worked problems on the solution of triangles and their areas 198
26.4 Further worked problems on the solution of triangles and their areas 200
26.5 Practical situations involving trigonometry 201
26.6 Further practical situations involving trigonometry 204
Assignment 12 206
27. Vectors 207
27.1 Introduction 207
27.3 Resolution of vectors 209 27.4 Vector subtraction 210
27.5 Relative velocity 212
28.1 Combination of two periodic functions 214
28.2 Plotting periodic functions 214
28.3 Determining resultant phasors by calculation 215
29. Number sequences 218
29.1 Simple sequences 218
29.2 The n’th term of a series 218
29.3 Arithmetic progressions 219
29.4 Worked problems on arithmetic progression 220
29.5 Further worked problems on arithmetic progressions 221
29.6 Geometric progressions 222
29.7 Worked problems on geometric progressions 223
29.8 Further worked problems on geometric progressions 224
Assignment 13 225
30. Presentation of statistical data 226
30.1 Some statistical terminology 226
30.2 Presentation of ungrouped data 227
30.3 Presentation of grouped data 230
31. Measures of central tendency and dispersion 235
31.1 Measures of central tendency 235
31.2 Mean, median and mode for discrete data 235
31.3 Mean, median and mode for grouped data 236
31.4 Standard deviation 237
31.5 Quartiles, deciles and percentiles 239
32. Probability 241
32.1 Introduction to probability 241
32.2 Laws of probability 241
32.3 Worked problems on probability 242
32.4 Further worked problems on probability 243
Assignment 14 246
33. Introduction to differentiation 247
33.1 Introduction to calculus 247
33.2 Functional notation 247
33.3 The gradient of a curve 248
33.4 Differentiation from first principles 249
33.5 Differentiation of y=axn by the general rule 250
33.6 Differentiation of sine and cosine functions 252
33.7 Differentiation of eax and ln ax 253
33.8 Summary of standard derivatives 254
33.9 Successive differentiation 255
33.10 Rates of change 255
34. Introduction to integration 257
34.1 The process of integration 257
34.2 The general solution of integrals of the form axn 257
34.3 Standard integrals 257
34.4 Definite integrals 260
34.5 Area under a curve 261