Engineering Mathematics Pocket Book PDF

Engineering Mathematics Pocket Book PDF

Download Engineering Mathematics Pocket Book PDF by John Bird free -From Engineering Mathematics Pocket Book: This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by students, technicians, scientists and engineers in day-to-day engineering practice. Buy from Amazon

Engineering Mathematics Pocket Book PDF

A practical and versatile reference source, now in its fourth edition, the layout has been changed and the book has been streamlined to ensure the information is even more quickly and readily available – making it a handy companion on-site, in the office as well as for academic study. It also acts as a practical revision guide for those undertaking BTEC Nationals, Higher Nationals and NVQs, where engineering mathematics is an underpinning requirement of the course.

All the essentials of engineering mathematics – from algebra, geometry and trigonometry to logic circuits, differential equations and probability – are covered, with clear and succinct explanations and illustrated with over 300 line drawings and 500 worked examples based in real-world application. The emphasis throughout the book is on providing the practical tools needed to solve mathematical problems quickly and efficiently in engineering contexts. John Bird’s presentation of this core material puts all the answers at your fingertips.

* A compendium of the maths essential to all engineering disciplines
* Succinct, easily accessible information, combined with comprehensive coverage – ideal for ongoing reference by both professional engineers and students alike
* New, improved structure to make information available even more quickly

Table of Content

Contents
Preface xi
1 Engineering Conversions, Constants and Symbols 1
1.1 General conversions 1
1.2 Greek alphabet 2
1.3 Basic SI units, derived units and common prefixes 3
1.4 Some physical and mathematical constants 5
1.5 Recommended mathematical symbols 7
1.6 Symbols for physical quantities10
2 Some Algebra Topics20
2.1 Polynomial division20
2.2 The factor theorem21
2.3 The remainder theorem23
2.4 Continued fractions24
2.5 Solution of quadratic equations by formula25
2.6 Logarithms28
2.7 Exponential functions31
2.8 Napierian logarithms32
2.9 Hyperbolic functions36
2.10 Partial fractions41
3 Some Number Topics46
3.1 Arithmetic progressions46
3.2 Geometric progressions47
3.3 The binomial series49
3.4 Maclaurin’s theorem54
3.5 Limiting values57
3.6 Solving equations by iterative methods58
3.7 Computer numbering systems65
4 Areas and Volumes73
4.1 Area of plane figures73
4.2 Circles77
4.3 Volumes and surface areas of regular solids82
4.4 Volumes and surface areas of frusta of pyramids and cones88
vi Contents
4.5 The frustum and zone of a sphere92
4.6 Areas and volumes of irregular figures and solids95
4.7 The mean or average value of a waveform101
5 Geometry and Trigonometry105
5.1 Types and properties of angles105
5.2 Properties of triangles106
5.3 Introduction to trigonometry108
5.4 Trigonometric ratios of acute angles109
5.5 Evaluating trigonometric ratios110
5.6 Fractional and surd forms of trigonometric ratios112
5.7 Solution of right-angled triangles113
5.8 Cartesian and polar co-ordinates116
5.9 Sine and cosine rules and areas of any triangle119
5.10 Graphs of trigonometric functions124
5.11 Angles of any magnitude125
5.12 Sine and cosine waveforms127
5.13 Trigonometric identities and equations134
5.14 The relationship between trigonometric and hyperbolic
functions 139
5.15 Compound angles141
6 Graphs149
6.1 The straight line graph149
6.2 Determination of law152
6.3 Logarithmic scales158
6.4 Graphical solution of simultaneous equations163
6.5 Quadratic graphs164
6.6 Graphical solution of cubic equations170
6.7 Polar curves171
6.8 The ellipse and hyperbola178
6.9 Graphical functions180
7 Vectors188
7.1 Scalars and vectors188
7.2 Vector addition189
7.3 Resolution of vectors191
7.4 Vector subtraction192
7.5 Relative velocity195
7.6 Combination of two periodic functions197
7.7 The scalar product of two vectors200
7.8 Vector products203
8 Complex Numbers206
8.1 General formulae206
8.2 Cartesian form206
Contents vii
8.3 Polar form209
8.4 Applications of complex numbers211
8.5 De Moivre’s theorem213
8.6 Exponential form215
9 Matrices and Determinants217
9.1 Addition, subtraction and multiplication of matrices217
9.2 The determinant and inverse of a 2 by 2 matrix218
9.3 The determinant of a 3 by 3 matrix220
9.4 The inverse of a 3 by 3 matrix221
9.5 Solution of simultaneous equations by matrices223
9.6 Solution of simultaneous equations by determinants226
9.7 Solution of simultaneous equations using Cramer’s rule230
9.8 Solution of simultaneous equations using Gaussian
elimination 232
10 Boolean Algebra and Logic Circuits234
10.1 Boolean algebra and switching circuits234
10.2 Simplifying Boolean expressions238
10.3 Laws and rules of Boolean algebra239
10.4 De Morgan’s laws241
10.5 Karnaugh maps242
10.6 Logic circuits and gates248
10.7 Universal logic gates253
11 Differential Calculus and its Applications258
11.1 Common standard derivatives258
11.2 Products and quotients259
11.3 Function of a function261
11.4 Successive differentiation262
11.5 Differentiation of hyperbolic functions263
11.6 Rates of change using differentiation264
11.7 Velocity and acceleration265
11.8 Turning points267
11.9 Tangents and normals270
11.10 Small changes using differentiation272
11.11 Parametric equations273
11.12 Differentiating implicit functions276
11.13 Differentiation of logarithmic functions279
11.14 Differentiation of inverse trigonometric functions281
11.15 Differentiation of inverse hyperbolic functions284
11.16 Partial differentiation289
11.17 Total differential292
11.18 Rates of change using partial differentiation293
11.19 Small changes using partial differentiation294
11.20 Maxima, minima and saddle points of functions of
two variables295
viii Contents
12 Integral Calculus and its Applications303
12.1 Standard integrals303
12.2 Non-standard integrals307
12.3 Integration using algebraic substitutions307
12.4 Integration using trigonometric and hyperbolic
substitutions 310
12.5 Integration using partial fractions317
12.6 The t tan θ
2
substitution319
12.7 Integration by parts323
12.8 Reduction formulae326
12.9 Numerical integration331
12.10 Area under and between curves336
12.11 Mean or average values343
12.12 Root mean square values345
12.13 Volumes of solids of revolution347
12.14 Centroids350
12.15 Theorem of Pappus354
12.16 Second moments of area359
13 Differential Equations366
13.1 The solution of equations of the form dy
dx f(x) 366
13.2 The solution of equations of the form dy
dx f(y) 367
13.3 The solution of equations of the form dy
dx f(x).f(y) 368
13.4 Homogeneous first order differential equations371
13.5 Linear first order differential equations373
13.6 Second order differential equations of the form
a d y
dx
b dy
dx cy 2
2 0 375
13.7 Second order differential equations of the form
a d y
dx
b dy
dx cy f(x) 2
2 379
13.8 Numerical methods for first order differential equations385
13.9 Power series methods of solving ordinary differential
equations 394
13.10 Solution of partial differential equations405
14 Statistics and Probability416
14.1 Presentation of ungrouped data416
14.2 Presentation of grouped data420
Contents ix
14.3 Measures of central tendency424
14.4 Quartiles, deciles and percentiles429
14.5 Probability431
14.6 The binomial distribution434
14.7 The Poisson distribution435
14.8 The normal distribution437
14.9 Linear correlation443
14.10 Linear regression445
14.11 Sampling and estimation theories447
14.12 Chi-square values454
14.13 The sign test457
14.14 Wilcoxon signed-rank test460
14.15 The Mann-Whitney test464
15 Laplace Transforms472
15.1 Standard Laplace transforms472
15.2 Initial and final value theorems477
15.3 Inverse Laplace transforms480
15.4 Solving differential equations using Laplace transforms483
15.5 Solving simultaneous differential equations using
Laplace transforms 487
16 Fourier Series492
16.1 Fourier series for periodic functions of period 2 π 492
16.2 Fourier series for a non-periodic function over range 2 π 496
16.3 Even and odd functions498
16.4 Half range Fourier series501
16.5 Expansion of a periodic function of period L504
16.6 Half-range Fourier series for functions defined over range L508
16.7 The complex or exponential form of a Fourier series511
16.8 A numerical method of harmonic analysis518
16.9 Complex waveform considerations522
Index525

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About the Author

John Bird, the author of over 100 textbooks on engineering and mathematical subjects, is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, U.K. More recently, he has combined freelance lecturing at Portsmouth University, with technical writing and Chief Examiner responsibilities for City and Guilds Telecommunication Principles and Mathematics, and examining for the International Baccalaureate Organisation. Engineering Mathematics Pocket Book PDF

John Bird is currently a Senior Training Provider at the Royal Naval School of Marine Engineering in the Defence College of Marine and Air Engineering at H.M.S. Sultan, Gosport, Hampshire, U.K. The school, which serves the Royal Navy, is one of Europe’s largest engineering training establishments.

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