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Preface | ||
Pt. 1 | Mathematics for Engineering | 1 |
1 | Indices, standard form and binary numbers | 3 |
2 | Errors, calculations and evaluation of formulae | 14 |
3 | Algebra | 23 |
4 | Simple equations | 40 |
5 | Simultaneous equations | 48 |
6 | Transposition of formulae | 58 |
7 | Quadratic equations | 65 |
8 | Logarithms and exponential functions | 74 |
9 | Areas and volumes | 86 |
10 | An introduction to trigonometry | 109 |
11 | The solution of triangles and their areas | 119 |
12 | Cartesian and polar coordinates | 129 |
13 | Straight line graphs | 133 |
14 | Reduction of non-linear laws to linear form | 144 |
15 | Graphs with logarithmic scales | 151 |
16 | Graphical solution of equations | 158 |
17 | Graphs of exponential, logarithmic and trigonometric functions and polar curves | 166 |
18 | Irregular areas and mean values of waveforms | 177 |
19 | Introduction to differentiation | 184 |
Pt. 2 | Further Mathematics for Engineering | 203 |
20 | Methods of differentiation | 205 |
21 | Differentiation of parametric equations | 215 |
22 | Applications of differentiation | 220 |
23 | Introduction to integration | 234 |
24 | Areas under and between curves | 242 |
25 | Mean and root mean square values | 251 |
26 | Volumes of solids of revolution | 255 |
27 | Centroids of simple shapes | 260 |
28 | Numerical integration | 269 |
29 | Solving equations by iterative methods | 277 |
30 | Arithmetic and geometric progressions | 282 |
31 | The binomial theorem | 289 |
Pt. 3 | Additional Mathematics for Engineering | 299 |
32 | Solution of first order differential equations by separation of variables | 301 |
33 | Introduction to second order differential equations | 311 |
34 | A numerical solution of differential equations | 316 |
35 | Vectors and phasors | 321 |
36 | Scalar and vector products | 332 |
37 | Trigonometric ratios, graphs, identities and equations | 339 |
38 | Compound angles | 359 |
39 | Angular properties of circles | 371 |
Pt. 4 | Extended Mathematics for Engineering | 379 |
40 | Functions and their curves | 381 |
41 | Integration using substitutions | 399 |
42 | Integration by parts | 417 |
43 | An introduction to complex numbers | 422 |
44 | The theory of matrices and determinants | 436 |
45 | The solution of simultaneous equations by matrices and determinants | 445 |
Answers to multi-choice questions | 454 | |
Index | 455 |
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