basic_engineering_mathematics0

Contents
ix
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 = ax n by the general rule 250
33.6 Differentiation of sine and cosine functions 252
33.7 Differentiation of e ax and ln ax 253
33.8 Summary of standard derivatives 254
33.9 Successive differentiation 255
33.10 Rates of change 255