678 Index
integration, using, 409–413
linear factors, 13–15, 409–411
quadratic factors, 16–17, 412–413
repeated linear factors, 17–19,
411–412
Particular solution of differential
equation, 445, 478
Particular integral, 483, 484
Pascal’s triangle, 58–59
Percentage component bar chart, 530
Percentile,546–547
Period, 139
Periodic function, 139, 186, 611, 630
combination of, 265–274
Periodic time, 143, 144
Perpendicular axis theorem, 385
Phasor, 143, 221, 267–274, 653–657
Pictogram, 530
Pie diagram, 530, 532
Planimeter, 203
Point of inflexion, 304
Poisson distribution, 559–561
Polar
co-ordinates, 117–121
curves, 180
form, 120, 121, 213, 218–221, 228
Poles, 598–599
Pole-zero diagram, 599
Pol/Rec function, 120, 220
Polynomial division, 6–8
Polynomial, Legendre’s, 512–514
Population, 529
Power series for ex, 28–29
coshxand sinhx, 49–50
Power series methods of solving
differential equations, 493–514
by Frobenius’s method, 500–506
by Leibniz-Maclaurin method,
497–500
Power waveforms, 173–176
Powers of complex numbers, 225–226
Practical trigonometry, 111–116
Precedence, 2, 3
Principal value, 219
Probability,548–553
laws of, 549
paper, 566
Product rule of differentiation,
292–293
Product-moment formula, 570–573
Pythagoras, theorem of, 97–98Quadrant, 122
Quadratic equations, 5–6
graphs, 178Quartiles, 546
Quotient rule of differentiation,
293–294Radian, 123, 144
Radius, 122
of curvature, 318, 319
of gyration, 384
Radix, 87
Rates of change, 299–300, 352–354
Reciprocal matrix, 236–237, 239–240
ratios, 99
Rectangular hyperbola, 180
Recurrence formula, 498
relation, 498, 507
Reduction formulae, 426–434
of exponential laws to linear form,
37–39
Regression, coefficients, 575
linear, 575
Relation between trigonometric and
hyperbolic functions, 159–162
Relative frequency, 529
velocity, 262–263
Remainder theorem, 10–12
Resolution of vectors, 254
Resultant phasor by complex numbers,
272
horizontal and vertical components,
270
phasor diagrams, 267
plotting, 265
sine and cosine rules, 268
Right-angled triangles, 105–108
R.m.s. values, 377–378
Rodrigue’s formula, 513
Roots of complex numbers, 226–228
Runge-Kutta method, 471–476Saddle point, 357–366
Sample, 529
Scalar product, 276–280
application of, 279
Scalar quantity, 251
Scatter diagram, 570, 578
Secant, 99
Sech, 41
Second moment of area, 383–391
Second order differential equations,
445, 477–492
Sector, 122
area of, 124–127
Segment, 122
Semicircle, 122
Semi-interquartile range, 546
Separation of variables, 445Series
binomial, 59–66
exponential, 28–29
Maclaurin’s, 68–74
sinh and cosh, 49–50
Set, 529
Simple equations, 3
Simpson’s rule, 204, 439–442
Simultaneous differential equations by
Laplace transforms, 605–609
Simultaneous equations, 4–5
by Cramers rule, 245
by determinants, 243–247
by Gaussian elimination, 246–247
by matrices, 241–243
Sine, 98
curves, 138–143
rule, 108
wave, 207
wave production, 137–138
Sineθsubstitution, 402–403
Sinh, 41
series, 49–50
Sinhθsubstitution,404–406
Sinusoidal form,Asin(ωt±α),
143–145
Small changes, 312–314, 354–356
Solution of any triangle, 109–116
right-angled triangles, 105–108
Space diagram, 262
Square wave, 146
Spectrum of waveform, 652–653
Standard curves, 178–181
derivatives, 290
deviation, 544–546
integration, 368
Stationary points, 304
Statistical tables, normal curve, 564
Straight line, 178
Sum to infinity, 55
Successive differentiation, 296–298
Symmetry relationships, 649–652Tables, statistical, normal curve, 564
Tally diagram, 534, 535, 537
Tangent, 98, 311–312
Tangential velocity, 282
Tanh, 41
Tanθsubstitution, 404
Taylor’s series, 462
Testing for a normal distribution,
566–569
Theorems
binomial, 59–66
Maclaurin’s, 68–76
Pappus, 381–383