| 584 MATHEMATICS FOR ENGINE ERS AND PIIYSICISTS |
| Parallelogram law of addition, 394 Parametcrs, 277, 280 intégrais containing, 167 variation of, 318 |
| Parametric équations, 143, 149, 150, 199, 215, 247 |
| Partial dérivatives, 125-143, 153 Partial differential équation, 350-391 |
| dérivation of, 351 |
| Fourier, 425 |
| intégration of, 353 |
| Laplace’s, 369, 382, 385, 386, 439 |
| linear, 357 |
| of elastic membrane, 377 of electric circuits, 386 of heat conduction, 367, 425 of vibratmg string, 361 Partial difîerentials, 128-143 Partial différentiation, 123-171 Partial fractions, method of, 297 Partial sum, 4 |
| Particular intégral, 290, 292, 297, 318, 359 |
| Particular solution, 230 Path, intégrais independent of, 208, 216, 452, 455 |
| Pendulum, simple, 44, 234-238, 306 Periodic function, 64 Picard’s method, 347 Plane, équation of, 147 mclined, 280, 282, 306 normal form for, 146 tangent, 146-149 Point, of inflection, 159 smgular, 451 Poisson formula, 512 Polar coordinates, 183,184, 276, 279, 386, 438 |
| Polygon, rectilinear, 478, 485 Polynomials, Legendre, 344, 384 Porous solids, drying of, 369 Potential, elcctrostatic, 487 gravitational, 219, 408 lines of equal, 277 Newtonian, 196 |
| velocity, 221, 222, 277, 430, 432, 453, 467, 480 |
| Potential function, 219, 411 Power sériés, 30-62 différentiation of, 33, 34 évaluation of intégrais by, 43-46 expansion in, 35-46 fonctions defined by, 33 intégration of, 33, 34 interval of convergence of, 31, 33 operations on, 33-35 theorems on, 31-35 umform convergence of, 33 uniqueness of expansion in, 38 whose ternis are infinité sériés, 40 Power séries solutions of differential équations, 325-346 Précision constant, 520, 521 Pressure on dam, 484 Primitive, 458 |
| Principal part of incrément, 128 Probability, 492-524 Probability curvo, 521 Probable error, 521 Probable value, most, 505 probability of, 511 Product, of déterminants, 110 scalar, 399 vector, 400 |
| Projection, Mercator’s, 479 stereographic, 479 Pulloy, slipping of belt on, 239 pv diagram, 223 |
| Q |
| Quadrature, meehanical, 554 Quotient, of complex numbers, 444 of power sériés, 40 |
| R |
| Radius of convergence, 31, 33 Radius vector, 195 Rank of matrix, 115 Ratio test, 11, 20, 31 Reaction, Chemical, 258 Rearrangement of sériés, 17 Rectilinear polygon, 478, 485 Recursion formula, 273, 328, 3 |