WDEX

581

Homogeneous équations, differential, 259, 261

linear algebraïc, 119-122 linear differential, 290 Homogeneous function, 136, 259 définition of, 136 Euler’s theorem on, 136 Hooke’s law, 241, 299 Horner’s method, 95 Hydrodynamics, 221, 422, 428-433, 480-484 Hyperbola, 247 Hyperbolic functions, 247-256 Hyperbolic paraboloid, 162

I

•

Imaginary roots, 94 Implicit functions, 132, 137-142 Inclined plane, 280, 282, 306 Incompressible fluid, 424, 430 Inconsistent équations, 105, 117-122 Independence, linear, 116, 317 of path, 208, 216, 452, 455 Independent events, 495 Independent trials, 501 Indicial équation, 334 Infinité sériés, 1-62

absolute convergence of, 16, 17, 20 conditional convergence of, 16, 17 définition of, 4 expansion m, 35-46, 155-158 of constants, 6-22 of functions, 23-62 of power functions, 30 of trigonométrie functions, 63-82 operations on, 21, 29, 33-35 sum of, 4n.

tests for convergence of, 9, 11, 12, 15, 20, 27, 31, 33

theorems on, 17, 21, 27, 28, 29, 31, 33, 34, 36, 38

umform convergence of, 23-30, 33 Inflection, point of, 159 Initial conditions, 235, 351 Intégral calculus, fundamental theorem of, 172, 457 Intégral curve, 226, 228, 279

Intégral équation, 347 Intégral formula, Cauchy’s, 461 Intégral test for sériés, 12 Intégral theorem, Cauchy’s, 455 Intégrais, around closed curve, 201, 203, 206, 216, 421 change of variable in, 183-188 defimte, 172

double, 173, 192, 202, 275 elliptic, 47-55, 238 évaluation of, by means of sériés, 43-46

iterated, 175, 180 line, 197-224, 410, 421, 454, 458 mean-value theorem for, 210n. multiple, 172-196 particular, 290, 292, 297, 318 surface, 188-196, 415, 421 transformation of (see Green’s theorem; Stokes’s theorem) triple, 177, 193 volume, 180, 415 witli a parameter, 47, 167 Integrating factor, 265 Intégration, by parts, 276 numerieal, 554—560 of complex functions, 453 of sériés, 29, 33, 34, 80 term by term, 33, 34, 80 Interpolation, method of, 101 Interpolation formulas, 550-554 Interval, 4

of convergence, 31, 33 of expansion, 38, 76 Inverse hyperbolic functions, 249, 255

Inversions, 106

Irrotational field, 418, 423, 430 Isolation of roots, 92 Isothermal process, 224 Iterated intégrais, 175, 180 Itération, method of, 297

J

Jn(x), 336

Jacobian, 141, 183, 190