576 MATHEMATICS FOR ENGINEERS AND PHYSICISTS

Cable, flexible, 244 flow of eleetricity in, 386 supportmg horizontal roadway, 242

Cartography, 479 Catenary, 247, 252. Cauchy-Riemann équations, 221, 450, 455

Cauchy’s équation, 322«.

Cauchy’s intégral formula, 461 Cauchy’s intégral test, 12 Cauchy’s intégral theorem, 455 Center of gravity, 177, 182, 183, 187, 190, 191, 196, 522

Change of variables, in dérivatives, 154

in intégrais, 183-188 Charactcristic équation, 292 Charge, distribution of, 487 Charts, distribution, 506 Chemical reaction, 258 Circular functions, 247 Circulation, of a liquid, 475, 477 of a vector, 418, 419 Closed curve, area of, 199-201 direction around, 200 intégral around, 201, 203, 206, 216, 421 simple, 200 en u, 51

Coefficients, Fourier, 65 metric, 437 Cofactor, 111, 112 Combinatory analysis, fundamental principle of, 493

Commutative law, 394, 399, 400 Comparison test for senes, 9 Complementary function, 290, 292 Complété elliptic intégrais, 48 Compiex number, 440 absolute value of, 441 argument of, 441 conjugate of, 444, 488 vector représentation of, 440 Compiex roots of unity, 87

Compiex variable, 440-491 functions of, 444-491 analytic, 451-491 dérivative of, 449 intégration of, 453 line intégral of, 454 Taylor’s expansion for, 464 Components of force, 217 Composite function, 134, 137 Condenser, 283, 299, 305, 308, 387 Conditionally convergent sériés, 16, 17, 21

Conditions, Cauchy-Riemann, 221, 450, 455 Dirichlet, 65

for exact differential, 212, 216 Conductivity, 367, 426 Conductor, 486, 489 Conformai mappmg, 465, 471 Conformai représentation, applications of, 479-491 Conformai transformation, 467 Conjugate of a compiex number, 444, 488

Conjugate functions, 468, 470 Conservation of matter, law of, 429 Conservative ficld of force, 219, 411 Consistent Systems of équations, 117-122

Continuity, équations of, 221, 429, 481

of functions, 23, 28, 124, 448 Contour lino, 144

Convergence, absolute, 16, 17, 20, 21, 33

conditional, 16, 17, 21 interval of, 31, 33 of sériés, 4, 7

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

radius of, 31, 33 umform, 23-30, 33 Cooling, law of, 254 Coordinate lines, 434 Coordinate surfaces, 434 Coordinates, curvilinear, 433-439 cylindrical, 152,185,190, 191, 378, 386, 434, 438

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