Région, multiply connected, 205, 212, 455

of intégration, 173 eimply connected, 205 Régula falsi, 101 Regular functions, 451 Remainder in Taylor’s sériés, 36-37 Remainder theorem, 92 Repeated trials, 501 Représentation, applications of conformai, 479-491 Rcsiduals, 534, 537 Résonance, 310 Riemann surface, 473 Right-handed System of axes, 397 Rod, flow of heat in, 373 vibiâtions of, 366, 367 Roots, of équations, 83-102 isolation of, 92 theorems on, 92-94 of umty, oi, a»2, 87 Rot (see Curl)

Rotational field, 418 Rule, Cramer’s, 113 Simpson’s, 556 trapézoïdal, .556

S

Scalar field, 406, 408 Scalar point funetion, 406, 418 Scalar product, 399 application of, 404 Scalars, 392

Schwartz transformation, 478, 485, 491

Seepage flow, 483 Séparation of variables, 257 Sequences, 2

fundam entai principle of, 6 limit of, 3

Sériés, asymptotic, 524 binomial, 40

évaluation of intégrais by, 43—46 Fourier, 63-82 infinité, 1-62

intégration and différentiation of, 29, 33, 34

Sériés, of constants, 6-22 of functions, 23-62 power, 30-62

solution of differential équations by, 228, 325-346

Taylor’s and Maclaurin’s, 37, 155, 228, 249, 464, 539 tests for convergence of, 9, 11, 12, 15, 20, 27, 31, 33

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

uniform convergence of, 23-30 Shearing stresses, 485 Simple closed curve, 200 Simple harmonie motion, 233, 301, 314, 380 équation of, 234 penod of, 234

Simple pendulum, 44, 234-238, 306 Simply connected région, 205 Simpson’s rule, 556 Simultaneous differential équations, 312-315

Simultaneous équations, 102-122, 139-141 sin x, 41, 250 siir ' x, 46

Sine, hyperbolic, 247 length of curve, 55 power sériés for, 40, 41 Sme senes, 73 Singular point, 451 Smgular solution, 279 Singulanties of funetion, 222 sinh x, 247

Sink (see Source and sink) Six-ordmate scheme, 548 Slipping of belt on pulley, 239 Small numbers, law of, 512 sn u, 51

Solenoidal field, 423 Solid angle, 195 Solids, drying of porous, 369 Solution, of cubic, 86-91

of differential équations, 226, 228, 325

general, 230, 290, 292, 350, 358 particular, 230