578 MATHEMATICS FOR ENGINEERS AND PHYSICISTS

Differential équations, general solution of, 230, 290, 292, 350, 358 homogeneous, 259, 261 homogcneous linear, 290 intégral curve of, 226, 228 integratmg factor of, 265 Laplace’s, 369, 382, 385, 386, 439, 451, 470, 481 Legendre’s, 342, 384 linear, 226, 283-349, 357 numerical solution of, 346 of electnc circuits, 301, 305, 386 of beat conduction, 367 of membrane, 377 of vibrating spring, 308 of vibrating string, 361 order of, 225 ordmary, 225-349 partial, 225, 350-391 partieular intégral of, 290, 292, 297, 318, 359 partieular solution of, 230 second order, 269, 295 séparation of variables in, 257 siinultaneous, 312-315 singular solution of, 279 solution ni senes, 228, 325, 349, 364

solution of, 226

witli constant coefficients, 287-315, 357

with variable coefficients, 284, 315-349

Differential expression, 225 Differential operators, 287-299, 357, 406

Différentiation, of implicit fonctions, 132-142

of senes, 29, 33, 34, 80 partial, 123-171 term by term, 33, 34, 80 under intégral sign, 167 Diffusion, 369, 427 Diffusivity, 368n.

Direction angles, 146, 398 Direction components, 146 Direction cosines, 146, 147, 151, 188, 194, 398

Direction ratios, 150, 151 Directional denvative, 143, 151, 219 (See also Gradient)

Dirichlet conditions, 65 Disoharge of condenser, 299 Discontinuity, fimte, 64 Discriminant of cubic, 89 Distance, élément of, 435 Distribution of charge, 487 Distribution charts, 506 Distribution turve, 504, 516 Distributive law, 399, 400 Divergence, of senes, 5, 8, 20 / of a vector, 411, 423, 438 Divergence theorem, 191, 415, 425, 428 dn u, 51

Dot product, 399

Double intégrais, 173, 192, 202, 275 Drying of porous solids, 369 Dynamics, laws of, 231

e, 42 e**, 250

Effects, superposition of, 129, 223 E{k, <p), 48-51, 54 Elastic curve, 240, 307 Elasticity, 241, 422, 484-486 Electrodynamies, 422, 423n. Electron, 315

Electrostatie field, 475, 477, 479 Electrostatic force, 487 Electrostatie potential, 487 Electrostatics, 486-491 Elément, of arc, 467 of area, 184, 190, 437 of distance, 435 of volume, 185, 187, 190, 437 Elcmentary functions, 315 expansion of, 35-46, 65-82, 465 Ellipse, area of, 177, 202 center of gravity of, 177 length of arc of, 47 Ellipsoidal coordinates, 433 Elliptic functions, 51