586 MATHEMATICS FOR ENGINEERS AND PHYSICISTS
Solution, of differential équations, singular, 279 of équations, 85-122 algebraic, 86, 95 graphical method of, 83 transcendental, 85, 97 of Systems of linear algebraic équations, 102-122 steady-state, 309, 310 Source and sink, 221, 411, 416, 424, 427, 429
Space curves, 149-152 Spherical coordinates, 152, 185, 382, 386, 434, 439 Spring, 299, 308, 313 oscillation of, 299 Standard déviation, 523 Steady heat flow, 256, 368, 369, 427 Steady-state solution, 309, 310 Stereographic projection, 479 Stirling’s formula, 508 Stokes’s theorem, 421 Stream function, 221, 432, 453, 481 Stream Unes, 277, 432, 467 Stresses, shearing, 485 String, vibration of, 361 Sum, of a sériés, An. of vectors, 393
Superposition of effects, 129, 223 Surface, équation of, 144 level, 406
normal to, 147, 407 Surface intégral, 188-196, 415, 421 Surfaces, coordinate, 434 Riemann, 473
Systems of équations, consistent or inconsistent, 117-122 linear algebraic, 107-122
T
Tangent line, 143, 147, 151 Tangent plane, 146-149 tanh, 249
Taylor’s formula, 35-46, 158 applications of, 41-46 Taylor’B sériés, 37, 464, 539 for functions of two variables, 155-158, 228
Taylor’s theorem, 36 Tension, 239, 243, 244, 251, 362, 377 Test, Cauchy’s intégral, 12 comparison, 9 for alternating sériés, 15 for sériés, 9, 11, 12, 15, 20, 27, 31, 33
ratio, 11, 20, 31 Weierstrass M, 27 Theory of lcast squares, 521 Thermodynamies, 222 Torque, 405
Total dérivatives, 130-143 Total differential, 127-143 Trajectories, orthogonal, 277-279 Transformation, by analytic fonctions, 467	'
conformai, 467 Green’s, 191, 202, 418 of element of arc, 467 of intégrais, 202 Schwartz, 478, 485, 491 Stokes’s, 421 Trapézoïdal rule, 556 Trials, rcpeated and independent, 501
Trigonométrie functions, 78, 251, 446, 447
Trigonométrie sériés, 63-82 Triple intégrais, 177, 193
U
Undetermined coefficients, 229 Uniform convergence, 23-30 test for, 27
Unit vectors, 394, 397 Unity, roots of, 87
V
Variable, change of, 154, 183-188 complex, 440-491 dépendent, 2 independent, 1
Variable heat flow, 368, 373, 425 Variation, of constants (see Variation, of parameters)