Index-H8152.tex 23/6/2006 15: 18 Page 723
INDEX 723Euler–Cauchy method, 465
Euler’s formula, 699
Euler’s method, 460
Even function, 43, 199, 669, 686, 695
Expectation, 545
Exponential form of complex number, 264
Fourier series, 690
Exponential function, 28, 193
graphs of, 31, 193
power series, 29
Extrapolation, 572Factorization, 2, 16
Factor theorem, 8
Family of curves, 443
Final value theorem, 636
First moment of area, 382
Formulae, 3, 705
Fourier coefficients, 658
Fourier series, 160, 657
cosine, 669
exponential form, 690
half range, 672, 680
non-periodic over range 2π, 663
over any range, 676
periodic of period 2π, 657
sine, 669
Frequency, 157, 527
curve, 559
distribution, 532, 533, 535, 559
domain, 698
polygon, 533, 535
relative, 527
spectrum, 698
Frobenius method, 498
Functional notation, 288
Function of a function, 295, 319
Functions of two variables, 355
Fundamental, 658Gamma function, 506
Gaussian elimination, 284
General solution of a differential equation, 444, 476
Geometric progression, 54
Gradient of a curve, 287
Graphs of exponential functions, 31
hyperbolic functions, 43
inverse functions, 333
logarithmic functions, 27
standard functions, 191
trigonometric functions, 148
Grouped data, 532, 539, 542
Growth and decay laws, 35Half range Fourier series, 672, 680
Half-wave rectifier, 163
Harmonic analysis, 160, 683
Harmonic synthesis, 160
Heat conduction equation, 515, 520
Hexadecimal number, 90Higher order differentials, 491
Histogram, 532, 535, 539
of probabilities, 555, 557
Homogeneous, 451, 475
Homogeneous first order differential equations, 451
Horizontal bar chart, 528
Hyperbola, 193, 314
rectangular, 193, 314
Hyperbolic functions, 41, 173
differentiation of, 330
graphs of, 43
inverse, 332
solving equations, 47
Hyperbolic identities, 44, 174
logarithms, 24, 33
Hypotenuse, 115
Hypotheses, 590Identities, hyperbolic, 44, 174
Identities, trigonometric, 166
Imaginary part, 249
Implicit differentiation, 319
Implicit function, 319
Independent event, 545
Indices, laws of, 1
Indicial equations, 26, 498
Industrial inspection, 554
Inequalities, simple, 12
involving a modulus, 13
involving quotients, 14
involving square functions, 15
quadratic, 16
Initial conditions, 512
Initial value theorem, 636
Integrating factor, 455
Integration, 367
algebraic substitution, 391
applications of, 374
areas, 374
centroids, 378
mean value, 376
r.m.s. value, 376
second moment of area, 382
volumes, 377
by partial fractions, 408
by parts, 418
change of limits, 393
coshθsubstitution, 405
definite, 371
numerical, 71, 433
reduction formulae, 424
sinθsubstitution, 401
sinhθsubstitution, 403
standard, 367
tanθsubstitution, 403
t=tan (θ/2) substitution, 413
trigonometric substitutions, 397
Interpolation, 572
Interval estimate, 581