Elliptio intégrais, 47-55 complété, 48

first kind, F(k, <p), 48-55, 238 second kmd, E{k, <p), 48-54 third kmd, II(w, k, <p), 50 Empirical formulas, 525-560 Entropy, 224 Envelope, 279 Equation, auxiliary, 292 Bernoulli’s, 286 Bessel’s, 332, 380 characteristic, 292 oubic, 86 Euler, 322 Fourier, 425 mdicial, 334 intégral, 347

Laplace’s, 195, 369, 382, 385, 386, 439, 451, 470, 481 Legcndre’s, 342, 384 of eontmuity, 221, 429, 481 of plane, 147 wave, 432

Equations, Cauchy-Biemann, 221, 450, 455

consistent, 117-122 dépendent, 105 difïerential, 225-391 Euler’s, 430

mconsistent, 105, 117-122 normal, 537, 540

parametric, 143, 149, 150, 199, 215 representmg spécial types of data, 528

simultaneous, 102-122, 139-141 solution of, 83-122 Systems of, 102-122

honïogeneous lmear, 119-122 non-homogeneous linear, 113-119

Error, Gaussian law of, 520, 536 mean, 516 mean absolute, 522 mean square, 522 of observation, 516 probable, 521 small, 56

Error function, 516

Euler équation, 322 Euler formulas, 78, 251 Euler’s équations, 430 Euler’s theorem, 136 Evaluation of intégrais, by différentiation, 169 m sériés, 43-46 Even function, 68 Events, dépendent, 495 indépendant, 495 mutually exclusive, 497 Exact difïerential, 211, 212, 216, 222, 224,262,411,418,420 Exact difïerential équation, 262 Expansion, m Bessel functions, 339 m Fourier sériés, 65-82 m Legendre polynomials, 346 in Maclaurm’s sériés, 37 in power sériés, 37-46 in Taylor’s sériés, 37 m trigonométrie sériés, 65 uniqueness of, 38 Expectation, 500

Expected number of successes, 508 Exponential form for trigonométrie functions, 78, 251, 446, 447 Exponential function, expansion for, 42, 446

Extremal values, 164 Extremum, 164

F

F(k, </>), 48-55 Factor, integrating, 265 Factor theorem, 92 Facto rial, n !, approximation for, 509 (See also Gamma functions) Falling body, 58, 232 Field, 406

conservative, 411 electrostatic, 475, 477, 479 irrotational, 418 Finite discontinuity, 64 Fittmg, curve, 525-560 Flexure, 298

Flow, of a liquid, 220, 424, 428, 477,

, 478,480-484