EERS AND PHYSICISTS

K

Ko(s), 337

L

Lagrange’s interpolation formula, 552

Lagrange’s method of multipliera, 163-167

Lamellar field, 423 Laplace’s approximation, 515 Laplace’s équation, 195, 369, 382, 385, 386, 439, 451, 470, 481 Law, Bernoulli-Euler, 241 binomial, 502, 512 of attraction, 218 of conservation of matter, 429 of cooling, 254 of dynamics, 231 of error, 520, 536 of gravitation, 232 of small numbers, 512 Least squares, method of, 536 theory of, 521

Legendre polynomials, 344, 384 expansion in, 346 Legendre’s équation, 342, 384 Leibnitz’s rule (see Différentiation, under intégral sign)

Leibnitz’s test (see Test, for altemat-mg sériés)

Length, of arc, 143 of ellipse, 47 of sine curve, 55 Level surface, 406 Limit, 2, 124, 454 Line, contour, 144 coordinate, 434

direction cosines of, 146, 147, 151 normal, 144, 146-149 of equal potential, 277 of flow, 475 stream, 277, 432, 467 tangent, 143, 147, 151 vector équation of, 395 Line intégrais, 197-224, 410, 421, 454

Line intégrais, applications of, 217-224

around a closed curve, 202, 206, 216, 421

définition of, 197, 454 évaluation of, 202-206, 458 for angle, 195 for area, 201 for work, 217 in space, 215, 410, 421 properties of, 206-217 transformation of, 202, 421 Linear dependence or independence, 116, 317

Linear differential équations, 288-349, 357

with constant coefficients, 287 357 with variable coefficients, 284, 315-349

Lmear differential operator, 287-299 Log z, 446

Logarithmic paper, 526 M

M test, 27

Maclaurin formula, 36 Maclaurin’s sériés, 37, 249 Magnitude of a vector, 393 Map, géographie, 479 of a curve, 466 Mapping functions, 467 Matrix, 114-122 augmented, 118 déterminants of, 115 rank of, 115

Maxima and minima, constramed, 163

for functions of one variable, 158 for functions of several variables, 160

Mean error, 516, 522 Mean-value theorems, 210n.

Measure numbers, 397 Mechanical quadrature, 554 Membrane, vibration of, 377 Mercator’s projection, 479 Metric coefficients, 437