Basic Engineering Mathematics By Jhon Bird Free eBOOK

Basic Engineering Mathematics By Jhon Bird

Author : Jhon Bird

Publication: ELSEVIER
Edition: 4^th

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

5.5 Hexadecimal numbers 33

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. Quadratic equations 69

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

11.6 Quadratic inequalities 80

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(ωt }α) 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 R→P and P→R functions on calculators 164

22. Areas of plane figures 166

22.1 Mensuration 166

22.2 Properties of quadrilaterals 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

27.2 Vector addition 207

27.3 Resolution of vectors 209 27.4 Vector subtraction 210

27.5 Relative velocity 212

28. Adding of waveforms 214

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

Assignment 15 265

List of formulae 266

Answers to exercises 270

Index 285

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