Index 677
Imaginary part, 213
Implicit differentiation, 320–324
Implicit function, 320
Independent event, 548
Indices, laws of, 1, 2
Indicial equations, 24–25, 501, 503,
507
Industrial inspection, 557–558
Initial conditions, 516
Initial value theorem, 591
Integrating factor, 456
Integration, 368
algebraic substitution,392–396
applications of, 375–391
areas, 375–376
centroids, 380–381
mean value, 377–378
r.m.s. value, 377–378
second moment of area, 383–391
t=tanθ/2 substitution, 414
volumes, 378–379
by partial fractions, 409–413
by parts, 420–425
change of limits, 395–396
coshθsubstitution,406–408
definite, 372–374
hyperbolic substitutions,399,
404–408
numerical, 73–74, 435–442
reduction formulae, 426–434
sineθsubstitution,402–404
sinhθsubstitution,404–406
standard, 368–374
tanθsubstitution, 404
t=tanθ/2 substitution,414–418
trigonometric substitutions,
398–404
Interpolation, 576
Inverse functions, 101, 188–190, 334
hyperbolic, 334
differentiation of, 341–344
trigonometric, 189, 334
differentiation of, 334–339
Inverse Laplace transforms, 593–597
using partial fractions, 596–597
Inverse matrix, 236
Irregular areas, 203
volumes, 205
Iterative methods, 77
Lagging angle, 140
Lamina, 380
Laplace’s equation, 515, 517, 518,
525–527
Laplace transforms, 582–586
common notations, 582
definition, 582
derivatives, 589–591
for differential equations, 600–604
for simultaneous differential
equations, 605–609
inverse, 593–597
using partial fractions, 596–597
linearity property, 582
of elementary functions, 582–585
properties of, 587
Laws of
growth and decay, 34–37
indices, 1, 2
logarithms, 22–24, 325
probability, 548
Leading angle, 140
Least-squares regression lines,
575–580
Leibniz
notation, 288
theorem, 495–497
Leibniz-Maclaurin method, 497–500
Legendre polynomials, 512–514
Legendre’s equation, 511–514
L’Hopital’s rule, 75
Limiting values,74–76
Linear
correlation, 570–574
first order differential equation,
456–460
regression, 575–580
second order differential equation,
477
velocity, 129–130
Logarithmic
differentiation, 325–329
forms of inverse hyperbolic
functions, 339–340
scale, 37
Logarithms, 20–26
graphs of, 25–26
laws of, 22–24, 325
Log-linear graph paper, 37
Log-log graph paper, 37
Lower class boundary value, 534Maclaurin’s series/theorem, 68–76
numerical integration, 73–74
Matrices, 231–240
adjoint, 239
determinant of, 235–236, 237–239
inverse, 236, 239–240
reciprocal, 236, 239–240
to solve simultaneous equations,
241–247transpose, 239
unit, 235, 236
Maximum point, 303
practical problems, 307–311
Mean value, 377–378, 541–543, 562
of waveform, 206–211
Measures of central tendency, 541, 544
Median, 541–543
Mid-ordinate rule, 203–204, 437–439
Minimum point, 303
practical problems, 307–311
Mode, 541–543
Modulus, 218, 277
Moment of a force, 282Napierian logarithms, 20, 31–34, 325
Natural logarithms, 20, 31–34, 325
Newton-Raphson method, 84–86
Non-homogeneous differential
equation, 477
Non-right angled triangles, 108
Norm, 277
Normal, 311–312
distribution, 562–569
equations, 575
probability curve, 562
probability paper, 566
Nose-to-tail method, 252
Numerical integration, 73–74, 435–442
methods for first order differential
equations, 461
Numerical methods, 146
for first order differential equations,
461–475
of harmonic analysis, 637–643Octal numbers, 87, 90–92
Odd function, 41, 43, 187–188, 623,
641, 649
Ogive, 535, 539, 546
Order of precedence, 2
Osborne’s rule, 45, 46, 161Pappus theorem, 381–383
Parabola, 178, 197, 315, 439
Parallel axis theorem, 384–385
Parallelogram method, 252
Parameter, 315
Parametric equations, 315–319
Partial differential equations, 515
Partial differentiation, 345–350
equations, 515–527
Partial integration, 515
Partial fractions, 13, 409
inverse Laplace transforms,
596–597