Basic Engineering Mathematics

Contents......Page 3
Preface......Page 7
Introduction......Page 9
Revision of addition and subtraction......Page 10
Revision of multiplication and division......Page 11
Highest common factors and lowest common multiples......Page 13
Order of operation and brackets......Page 15
Introduction......Page 17
Adding and subtracting fractions......Page 18
Multiplication and division of fractions......Page 20
Order of operation with fractions......Page 22
Converting decimals to fractions and vice versa......Page 25
Significant figures and decimal places......Page 27
Adding and subtracting decimal numbers......Page 28
Multiplying and dividing decimal numbers......Page 29
Adding, subtracting, multiplying and dividing......Page 31
Further calculator functions......Page 33
Evaluation of formulae......Page 37
Introduction......Page 43
Percentage calculations......Page 44
Further percentage calculations......Page 45
More percentage calculations......Page 47
Introduction......Page 51
Ratios......Page 52
Direct proportion......Page 54
Inverse proportion......Page 58
Powers and roots......Page 60
Laws of indices......Page 62
SI units......Page 67
Common prefixes......Page 68
Standard form......Page 71
Engineering notation......Page 73
Metric conversions......Page 75
Metric – US/Imperial conversions......Page 78
Introduction......Page 84
Basic operations......Page 85
Laws of indices......Page 88
Brackets......Page 92
Factorisation......Page 94
Laws of precedence......Page 95
Solving equations......Page 98
Practical problems involving simple equations......Page 102
Transposing formulae......Page 110
Further transposing of formulae......Page 112
More difficult transposing of formulae......Page 115
Solving simultaneous equations in two unknowns......Page 119
Further solving of simultaneous equations......Page 121
Solving more difficult simultaneous equations......Page 123
Practical problems involving simultaneous equations......Page 125
Solving simultaneous equations in three unknowns......Page 129
Introduction......Page 132
Solution of quadratic equations by factorisation......Page 133
Solution of quadratic equations by ‘completing the square’......Page 135
Solution of quadratic equations by formula......Page 137
Practical problems involving quadratic equations......Page 138
Solution of linear and quadratic equations simultaneously......Page 141
Introduction to logarithms......Page 142
Laws of logarithms......Page 144
Indicial equations......Page 147
Graphs of logarithmic functions......Page 148
Introduction to exponential functions......Page 149
The power series for......Page 150
Graphs of exponential functions......Page 152
Napierian logarithms......Page 154
Laws of growth and decay......Page 157
Axes, scales and co-ordinates......Page 164
Straight line graphs......Page 166
Gradients, intercepts and equations of graphs......Page 169
Practical problems involving straight line graphs......Page 176
Determination of law......Page 183
Revision of laws of logarithms......Page 186
Determination of laws involving logarithms......Page 187
Graphical solution of simultaneous equations......Page 192
Graphical solution of quadratic equations......Page 194
Graphical solution of cubic equations......Page 198
Logarithmic scales and logarithmic graph paper......Page 201
Graphs of the form......Page 202
Angular measurement......Page 211
Triangles......Page 217
Congruent triangles......Page 221
Similar triangles......Page 223
Construction of triangles......Page 225
The theorem of Pythagoras......Page 228
Sines, cosines and tangents......Page 231
Evaluating trigonometric ratios of acute angles......Page 233
Solving right-angled triangles......Page 235
Angles of elevation and depression......Page 239
Graphs of trigonometric functions......Page 244
Angles of any magnitude......Page 245
Terminology involved with sine and cosine waves......Page 248
Sinusoidal form:......Page 251
The sine and cosine rules......Page 254
Workedproblemsonthesolution of triangles and their areas......Page 255
Further worked problems on the solution of triangles and their areas......Page 257
Practical situations involving trigonometry......Page 258
Further practical situations involving trigonometry......Page 260
Changing from Cartesian to polar co-ordinates......Page 263
Changing from polar to Cartesian co-ordinates......Page 265
Use of Pol/Rec functions on calculators......Page 266
Common shapes......Page 274
Areas of common shapes......Page 277
Areas of similar shapes......Page 284
Properties of circles......Page 286
Radians and degrees......Page 288
Arc length and area of circles and sectors......Page 289
The equation of a circle......Page 293
Volumes and surface areas of common shapes......Page 297
More complex volumes and surface areas......Page 304
Volumes and surface areas of frusta of pyramids and cones......Page 310
Volumes of similar shapes......Page 314
Areas of irregular figures......Page 315
Volumes of irregular solids......Page 318
Mean or average values of waveforms......Page 319
Scalars and vectors......Page 325
Drawing a vector......Page 326
Addition of vectors by drawing......Page 327
Resolving vectors into horizontal and vertical components......Page 329
Addition of vectors by calculation......Page 330
Vector subtraction......Page 334
Relative velocity......Page 335
notation......Page 336
Combining two periodic functions......Page 338
Plotting periodic functions......Page 339
Determining resultant phasors by drawing......Page 340
Determining resultant phasors by the sine and cosine rules......Page 342
Determining resultant phasors by horizontal and vertical components......Page 343
Presentation of statistical data......Page 351
Some statistical terminology......Page 352
Presentation of ungrouped data......Page 353
Presentation of grouped data......Page 356
Measures of central tendency......Page 363
Mean, median and mode for discrete data......Page 364
Mean, median and mode for grouped data......Page 365
Standard deviation......Page 366
Quartiles, deciles and percentiles......Page 368
Probability......Page 370
Introduction to probability......Page 371
Laws of probability......Page 372
Functional notation......Page 380
The gradient of a curve......Page 381
Differentiation from first principles......Page 382
by the general rule......Page 383
Differentiation of sine and cosine functions......Page 386
and......Page 388
Summary of standard derivatives......Page 389
Rates of change......Page 390
Differentiation of a product......Page 392
Differentiation of a quotient......Page 393
Function of a function......Page 394
The process of integration......Page 396
Standard integrals......Page 397
Definite integrals......Page 400
The area under a curve......Page 402
Simple sequences......Page 411
th term of a series......Page 412
Arithmetic progressions......Page 413
Geometric progressions......Page 416
Introduction......Page 420
Binary numbers......Page 421
Octal numbers......Page 424
Hexadecimal numbers......Page 427
Introduction to inequalities......Page 431
Inequalities involving a modulus......Page 432
Inequalities involving quotients......Page 433
Inequalities involving square functions......Page 434
Quadratic inequalities......Page 435
Chapter 2......Page 444
Chapter 4......Page 445
Chapter 7......Page 446
Chapter 8......Page 447
Chapter 10......Page 448
Chapter 12......Page 449
Chapter 14......Page 450
Chapter 16......Page 451
Chapter 19......Page 452
Chapter 21......Page 453
Chapter 23......Page 454
Chapter 26......Page 455
Chapter 29......Page 456
Chapter 32......Page 457
Chapter 34......Page 458
Chapter 35......Page 459
Chapter 37......Page 460
Chapter 39......Page 461
Index......Page 464