INDEX

A

Absolute convergence of sériés, 16,

17, 20, 21

Absolute value of coniplex number,

441

Addition, of séries, 21 of vectors, 393 parallelogram law of, 394 Adiabîftic process, 224 Aerodynamics, 133, 431 Algebra, fondamental theorcm of, 92 Algebraic theorems, 92-94 Alternatmg séries, 15 am «, 51

Arapere’s formula, 52ra.

Amplitude of coniplex number, 441 Amplitude function, 51 Analysis, harmonie, 545 Analytic functions, 451-491 Angle, as a line intégral, 195 direction, 146, 398 of lap, 240 of twist, 485 solid, 195

Angular veloeity, 61, 191, 236, 404,

424

Applications, of conformai représentation, 479-491 of lme intégrais, 217-224 of scalar and vector produets, 404-406

Approxnnate formula, for n\, 509 for probability of most probable number, 511

in applied mathematics, 55 Approximation, Laplace’s or normal,

515

Approximations to binomial law, 512 Arc length, 143 of ellipse, 47

Arc length, of sinusoid, 55 Area, 172

as a double intégral, 178 as a lme intégral, 199-202 element of, 183, 184, 190, 437 positive and négative, 200 surface, 188-196

Argument of complex number, 441 Associative law, for sériés, 18 for vectors, 394

Asymptotic formula for ■«', 509 Asymptotic séries, 524 Atmosphère, thickness of, 61 Attraction, law of, 218, 232 motion under, 58, 218 of cône, 196 of eyhnder, 196 of sphere, 196, 232 Augmented matrix, 118 Auxiliary équation, 292 Averages, method of, 534 Axes, right- or left-handed, 397

B

Base vectors, 396 Beam, 240-242, 307 Belt on pulley, slippmg of, 239 Bendmg moment, 241 Bernoulli-Euler law, 241, 307 Bernoulli’s équation, 286 Bessel functions, 273, 336, 381 expansion in, 339 Bessel’s équation, 332, 380 Beta function, 276 Binomial law, 502

approximations to, 512 Binomial sériés, 40 Biot and Savart, law of, 52 Boundary conditions, 242, 351, 363, 370

Buckling, 299

518