INDEX

577

Coordinates, ellipsoidal, 433 parabolie, 439

polar, 183, 184, 276, 279, 386, 438 spherical, 152, 185, 382, 386, 434, 439

cos x, 46, 250 cosh, 247

Cosine, hyperbolic, 247 powcr sériés for, 38, 40 Cosine séries, 73

Cosines, direction, 146, 147, 151, 188, 194, 398 coth, 249 Cramer’s rule, 113 Cross product, 400 Cubic équation, algebraic solution of,*86

graphical solution of, 83 Curl, 418, 422, 423, 438 Current, 386, 427 Curve, distribution, 504, 516 elastic, 240, 307 map of, 466 Curve fitting, 525-560 Curves, intégral, 226, 228, 279 orthogonal, 277, 468 Curviiinear coordinates, 433-439 Cylinder functions (see Bessel func-tions)

Cylmdrical coordinates, 152, 185, 190, 191, 378, 386, 434, 438

D

Dam, gravity, 483 Dampmg, viscous, 30ü Dead-beat motion, 304 Décomposition of vectors, 396 Definite intégrais, 172

change of variable in, 183-188 évaluation of, 172 mean-value theorem for, 210n. Deflection, 299

Degree of differential équation, 225 Del, V (see Nabla)

Delta amplitude, dn, 51 De Moivre’s theorem, 90, 442

Dependence, functional, 2 linear, 116

Dépendent events, 495 Dérivation of differential équations, 231-247 Dérivative, 125 directional, 143, 151, 219 normal, 144, 146, 152 of functions of a complex variable, 449, 452, 463

of hyperbolic functions, 255 of senes, 29, 33 partial, 125-143, 153 total, 130-143 Descartes’s rule of signs, 94 Déterminants, 102-114 cofactors of, 111 expansion of, 106n., 111 functional or Jacobian, 183 Laplace development of, 111 minors of, 110 of matrix, 115 product of, 110 properties of, 107-112 solution of équations by, 102-114 Wronskian, 317 Déviation, standard, 523 Diagonal term of déterminant, 107 Diagram, pv, 223 Différences, 527

Differential, exact, 211, 212, 216, 222, 224, 262, 411, 418, 420 of area, 184, 190 of volume, 185, 187, 190 partial, 128-143 total, 127-143

Differential équations, 225-391 Bernoulli’s, 286 Bessel’s, 332, 380 Cauchy-Riemann, 221, 450, 455 Cauchy’s, 322n. définition of, 225 degree of, 225 dérivation of, 231-247 Euler’s, 322, 430 exact, 262 first order, 256, 267 Fourier, 425

520