|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Sokolnikoff I.S. — Mathematics of Physics and Modern Engineering |
|
|
|
| Предметный указатель |
Particular integrals 7
Particular integrals by method of undetermined coefficients 59
Particular integrals by variation of parameters 72
Pendulum 48 49 85p
Period of oscillations 44 81 84
Period of pendulum 49 85p
Period of vibration 443
Period of waves 428
permutations 611
Phase of simple harmonic motion 41
Picard’s method 509
Piecewise continuity 755
Piecewise smoothness 206 372
Plancherel’s theorem 483n
Plane, equation of 306
Plane, osculating 311
Plane, tangent 277n 309
Point at infinity 577
Point set 773
Point set, measure of 771
Point vortex 591
Points in n-dimensional space 316
Points in sample space 613
Poisson’s distribution 633
Poisson’s equation 268 111n 495
Poisson’s equation, uniqueness of solution of 199p
Poisson’s formula 195
Poisson’s formula for a circle 470 599/?.
Poisson’s formula for a half plane 490
Poisson’s formula for a half space 503
Poisson’s law of probability 651
Poles of analytic functions 570 574
Poles of analytic functions, residues at 571
Poles of analytic functions, simple 570
Polynomial representation of data 694 702
potential energy 43
Potential energy, principle of minimum 264
Potential theory 468 (see also “Dirichlet’s problem” “Neumann’s
Potential, complex 587
Potential, electrostatic 467 496
Potential, gravitational 409 468
Potential, Newtonian 277p 409
Power series 138
Power series, Abel’s theorem on 142
Power series, convergence of, absolute and uniform 139
Power series, convergence of, radius of 142 170 562
Power series, differentiation and integration of 140
Power series, evaluation of integrals by 117
Power series, expansions in 114 561
Power series, multiplication of 142
Power series, solution of differential equations by 153
Power series, substitution in 152
Power series, uniqueness of representation by 141 146
Precision constant 662 670
Pressure in star’s interior 48
Pressure on gravity dam 593
Pressure, atmospheric 50
primitive 551
principal argument 528
Principal normal 311
Principal value of improper integrals 602
Principal value of log Z 537
probability 610 611 652
probability density 632 634
Probability density, Gauss’ 633
Probability density, joint 634
Probability density, Maxwell — Boltzmann’s 633
Probability density, Poisson’s 633
Probability integral, table of 776
Probability, binomial law of 639 647
Probability, compound and total, theorems on 617 635
Probability, events in 610 618 619 638
Probability, Laplace’s law in 617
Probability, law of small numbers (Poisson’s) 654
Probability, law ol large numbers 651
Probability, marginal 625
Probability, normal law of 647 653
Probable error 662
Probable value 635
Product of determinants 325 745
Product of matrices 328
Product of vectors 293 295 298
Projectiles 50
Pulley, slipping of belt on 11
Pursuit curves 33
Pythagorean formula 322
Quadratic forms 347
Quadratic forms, differential 362
Quadratic forms, positive definite 349
Quadrature 715
Radiation condition 501
Radiation from antenna 486
Radius of convergence 139 170 562
Random molecular motions 653n
Random process 622
Random variables 623 662
Random walks 653
Rank of a matrix 330 750
Ratio Test 125
Rational number 772
Reflection, law of, 297p
Reflection, transformation of 341
Refraction, law of 297p
Regions, bounded 535
Regions, closed 218 535
Regions, connected 383
Regions, connected, multiply 383 535
Regions, connected, simply 383 535
Regions, finite 535
Regions, open 218
Regions, regular 383
Relative frequency 615 638 642
Remainder in Taylor’s series 144
Residuals 703
Residue theorem 573
Residue theorem, evaluation of real integrals by 599
Residues 571
Resonance 86 89 453
resonant frequency 89 477
Riemann function 508
Riemann integral 771
Riemann’s mapping theorem 586
Rocket, motion of 45 46p
Rocket, thrust 45
Rodrigues’ formula 159p
Roots of unity 532
Rotation, of shaft, critical speed of 94
Rotation, transformation of 341
Rotation, velocity of 399p
Sample space 613 634
scalar 287
Scalar fields 367
Scalar product 293n 319
Scalar triple product 297
Schwarz — Christoffel mapping formula 599
Schwarz’ inequality 322
Seidel’s method 689
Separation of variables 18 459 732
Series 111
Series of complex terms 169
Series of orthogonal functions 195
Series, addition of 117
Series, alternating 128
Series, basic properties of 116
Series, binomial 155
Series, Cauchy’s criterion for 115
Series, comparison tests for 122 125 134
Series, convergence of 112
Series, convergence of, absolute 127 170
Series, convergence of, conditional 129
| Series, convergence of, fundamental principle for 114
Series, convergence of, in the mean 200
Series, convergence of, pointwise 204
Series, convergence of, tests for, comparison 113 122
Series, convergence of, tests for, integral 118
Series, convergence of, tests for, Leibniz’ 128
Series, convergence of, tests for, ratio 125
Series, convergence of, uniform 132 136
Series, convergence of, uniform, Weierstrass test for 134
Series, differentiation of 135
Series, evaluation of integrals by 147
Series, Fourier see “Fourier series”
Series, geometric 115
Series, harmonic 113
Series, integration of 135
Series, Laurent’s 565
Series, Maclaurin’s 144
Series, multiplication of 131
Series, power see “Power series”
Series, rearrangement of 129
Series, remainder in 113
Series, solution of differential equations by 153 455
Series, sum of 112
Series, sum of, partial 111
Series, Taylor’s 144 561
Series, telescoping 116p
Series, trigonometric see “Fourier series”
Shaft, critical speed of rotation 94
Shearing load 435p
Significance level 649
Similar transformations 339
Similitude, principle of 433
Simple closed curve 383n
simple harmonic motion 44
simple pendulum 48
Simply connected region 383
Simpson’s rule 717
Singular integral 493
Singular points 543 569
Singular points, essential 570 574
Singular points, isolated 569
Singular solutions of differential equations 34
Sink 384 591
Solenoidal field 402
Solid angle 399p
Solution of differential equations see “Ordinary differential equations” “Partial
Sommerfeld’s radiation condition 501
Sound, equation of propagation of 420
Sound, velocity of 435p
Source 384 591
Source of heat 489 504 653
Space curves (Frenet — Serret formulas) 312
Space, complex 322
Space, dimensionality of 317
Space, Euclidean 321 374n
Space, linear vector 316
Space, sample 613 634
Specific heat 415
Spectral theory 199
Spherical coordinates 360 367p
Spring, oscillation of 80 82 86 88 99
Stability of columns 91
Stability of rotating shafts 92
Stability of solutions of differential equation 103 105
Stagnation points 590
Standard deviation 661 669
Standard deviation of the mean 667
Standard deviation, unbiased estimate of 670
Statistical hypothesis 614
Statistical hypothesis, relation to significance level 649
Steady-state solutions 88 765
Steady-state temperature 457 471
Stieltjes integral 630
Stirling’s formula 644
Stokes’ Theorem 400 402p
Stream function 413
Streamlines 413 414p 587
String, vibration of 425 431—454 484
Sturm — Liouville theory 109
Summation convention 324
Superposition principle 766
Surface integrals 277 373
Surface, level 369
Surface, normal to 309 369 373n
Surface, one-sided 383
Surface, piecewise smooth 277 383
Surface, regular 384
Surface, tangent plane to 277n 309
Surface, two-sided 277 373n 383
Systems of equations, differential 95 733
Systems of equations, linear algebraic 350 687 689 749
Tangent line 301 311
Tangent plane 277n 309 311
Tautochrone 767
Taylor’s Formula 143
Taylor’s formula for functions of several variables 257
Taylor’s formula, approximations by 149
Taylor’s series 144 561
Telegrapher’s equation 514
thermal conductivity 415 455
torque 303 (see also “Moment”)
Torsion 312
Total differential 226 234
Total probability 618 635
Transcendental equations 677 679 684
Transforms, Fourier 191
Transforms, Laplace 754
Trapezoidal rule 717
Trigonometric functions 172 536
Undetermined coefficients, method of 59
Uniform convergence 132
Uniqueness of representation in Fourier series 186
Uniqueness of representation in Laurent’s series 567
Uniqueness of representation in power series 141 146
Uniqueness of solutions of ordinary differential equations 7 38 157
Uniqueness of solutions of partial differential equations 505—510
Unit impulse 759
Unit vectors see “Base vectors”
Unitary matrices 343p 350
Unitary transformations 343p
Value of logarithmic function 537
Value, absolute, of complex numbers 168 528
Value, characteristic 344 507p 732
Value, expected 623 639
Value, extreme 250 264
Value, maximum, of harmonic function 499p 506 558 561
Value, median 637p
Value, principal, of improper integrals 602
Value, probable 635
Variance 664 669
Variation 265
Variation of parameters 72
Vector acceleration 302p 313 367p
Vector analysis 285—351 (see also “Vector field theory”)
Vector field theory 355—420
Vector functions, continuity of 299 368
Vector functions, line integrals of 374
Vector product 295
Vector spaces 316 323
Vector, velocity 301 367p
Vectors, algebraic operations on 288—298 316—324
Vectors, base or coordinate see “Base or coordinate vectors”
Vectors, bound 288
Vectors, characteristic 344
Vectors, components of 291 317 321
Vectors, continued products of 297
Vectors, coordinate 319
Vectors, differentiation of 299
Vectors, free 288
Vectors, linear dependence of 317
|
|
|
| Реклама |
|
|
|
|
|
О проекте