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| Sokolnikoff I.S. — Mathematics of Physics and Modern Engineering |
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| Предметный указатель |
Differential, exact 22b 380
Differential, total 226 234
Differentiation numerical 698
Differentiation of analytic functions 542
Differentiation of composite functions 230
Differentiation of definite integrals 261
Differentiation of determinants 743
Differentiation of Fourier series 210
Differentiation of implicit functions 230 235
Differentiation of infinite series 135
differentiation of power series 140
Differentiation of vector functions 299
Differentiation partial 219
Differentiation, chain rule for 228
Diffusion 14 416 463n
Diffusivity 463n
Dimensional analysis 433
Dipole 408p 496
Dirac’s delta function 761
Dirac’s distribution 759
Direction cosines 370
Directional derivative 243 253 369
Dirichlet’s conditions 180
Dirichlet’s kernel 205
Dirichlet’s problem 467 502 511 595
Dirichlet’s problem for a circle 469
Dirichlet’s problem for a half plane 484
Dirichlet’s problem for a half space 503
Dirichlet’s problem for arbitrary regions 595
Dirichlet’s Theorem 180
Discontinuity, simple 178
Discrete distributions 627 628
Discrete variables 628
dispersion 427
Distribution function 632
Distributions, binomial 639 640p
Distributions, bivariate 666
Distributions, continuous 631
Distributions, discrete 627 628
Distributions, Gaussian 633
Distributions, Maxwell — Boltzmann’s 633
Distributions, Normal 633 651
Distributions, Poisson’s 633
Divergence 384
Divergence in cartesian coordinates 386
Divergence in curvilinear coordinates 406
Divergence theorem 388 493
Dot product see “Scalar product”
Double layer 497
Dummy or summation index 324
Dynamics, laws of 302
D’Alembert’s solution of wave equation 439 485
e 655n
Eigenfunction (characteristic function) 732
Eigenvalue (characteristic value) 341 507p 732
Eigenvector (characteristic vector) 314
Elastic curve 16 86p
Elastic curve, curvature of 16
Elasticity 599
Electric circuits 81 87 100 756
Electromechanical analogies 81
Electron, acceleration of 45 46p
Electron, mass-to-charge ratio 100p
Electrostatic field 592 594
Electrostatics 407 496
Ellipse, length of 147
Elliptic differential equation 505
Elliptic differential equation, difference equation for 511 518
Elliptic integrals 49 86p 148
Emissivity 463
Empirical formulas 701
Energy, conservation of 43 48
Energy, kinetic 43 306p
Energy, potential 43 264
Envelope 35
Equation of continuity 412 417
Error function (probability integral), table 776
Errors, estimate of 658 660
Errors, Gauss’ law of 662
Errors, in solving differential equations 38 104
Errors, mean-absolute 662
Errors, mean-square 662
Errors, probable 662
Errors, theory of 658
Essential singular points 570 574
Estimate of errors 658 660
Estimate of variance 669
Estimate, maximum likelihood 610 660
Estimate, reliability of 670
Estimate, unbiased 610
Euclidean space 321 371n
Euler — Fourier formula 175 196
Euler’s critical load 92
Euler’s differential equation 78
Euler’s differential equation, invariational calculus 267
Euler’s formula for exponentials 173 536
Euler’s formula for Fourier coefficients 175 196
Euler’s hydrodynamical equations 419
Euler’s polygonal curves 721 727
Euler’s theorem on homogeneous functions 231
Even functions 183
Even functions, Fourier expansion for 181
Events in probability 610 618 619 638
Exact differential 220 380
exact differential equations 20
Expansion in power series 144
Expansion in series of orthogonal functions 201
Expansion of determinants 326 741
Expansion, adiabatic 50p
Expansion, Fourier 175 196
Expansion, Heaviside 766
Expansion, Laurent 561 565
Expansion, Maclaurin 144
Expansion, Taylor 144
Expectation 623 634
Expectation of product 663
Expectation of sum 624
Expected frequency 627
Expected value 623 639
Exponential function 172 536 581
Extrapolation formulas 696
extreme values 250 264
Extremum 250
Factor, integrating 22
Factorial function 162 755
Factorial, n!, approximation for 644
Falling bodies 47
Fermat’s principle 264
Field 367
Field theory 355—420
Field, conservative 408
Field, electrostatic 467 496 592 594
Field, gravitational 409 467
Field, irrotational 402
Field, solenoidal 402
Finite differences, method of 734
Flexural rigidity 93
Fluid flow 411 416 587—595
Fluid flow under dam 593
Fluid flow, ideal 419 587 592
Fluid flow, irrotational 412 588
Fluid flow, out of channel 594
Fluid flow, solenoidal 412
Fluid flow, stagnation points in 590
Fluid flow, steady 412 587
Fluid flow, uncompressible 412 418
Fluid flow, vortex in 591
Flux 384
Force field 408
Force field, electrostatic 467 496 592 594
| Force field, gravitational 409
Forced vibrations 86 451
Fourier coefficients 175 196
Fourier coefficients, bounds for 211
Fourier coefficients, Parseval’s equality for 202 204p
Fourier expansion 175 196
Fourier expansion for odd functions 185
Fourier heat equation 414
Fourier integral equation 192
Fourier integrals 190 194
Fourier series 175 196
Fourier series, complex form of 192
Fourier series, convergence of 200 204
Fourier series, differentiation of 210
Fourier series, double 476
Fourier series, extension of interval for 187
Fourier series, for even and odd functions 184
Fourier series, integration of 207
Fourier series, uniqueness theorem for 186
Fourier transform 194 482—490
Free vibrations 79 432 444 446 475
Frenet — Serret formulas 312
Frequency equation 478 481
Frequency function 627
Frequency function, binomial 639
Frequency, characteristic 477 479p 482p
Frequency, relative 615 638 642
Frequency, resonant 89 477
Fresnel integrals 147 153p
Fuchs’ Theorem 157
Fundamental theorem of integral calculus 9 261 550
Gamma function 149p 162
Gas, ideal 221
Gas, viscosity of 451
Gauss — Jordan reduction 687n
Gauss — Seidel method 689n
Gauss’ distribution 633
Gauss’ divergence theorem 388
Gauss’ law of errors 662
Gauss’ reduction method 350n 687
Geometric series 115
Gradient in cartesian coordinates 370
Gradient in curvilinear coordinates 407
Gradient,  244 307 390
Graeffe’s root-squaring method 679n
Gram — Schmidt method 351
Graphical solution of equations 678
Gravitational attraction 277p 409
Gravitational attraction, motion under 47 49p
Gravitational constant 46
Gravitational field 407
Gravitational potential 409
Gravity dam 593
Gravity, center of 275 281
Greatest lower bound 773
Green’s function 501
Green’s function for half space 502
Green’s identities 391p 493
Green’s theorem in plane 391 402p
Green’s theorem, symmetric forms of 391p 493
Growth factor 418
Harmonic analysis 711
Harmonic function 468 560 585
Harmonic function, average value theorem for 498
Harmonic function, conjugate 560 588
Harmonic function, differentiability of 559
Harmonic function, maximum values of 499p 506 558 561
Harmonies 177
heat capacity 455
Heat equation 414 455
Heat equation, solution of, by integrals 482
Heat equation, solution of, by separation of variables 459
Heat equation, solution of, by series 455—171
Heat equation, solution of, uniqueness of 466 506
Heat flow 414 455—467 483 504 512
Heat flow in a rod 456—466 489 769
Heat flow in a sphere 471
Heat flow, connection with random walks 653
Heat flow, source function for 491 653
Heat source 489 504 653
Heaviside’s expansion theorem 766
Helix 314 316p
Helmholtz formula 499
Hermitian form 348
Hermitian matrix 349
Holomorphic function 513
homogeneous differential equations see “Ordinary differential equations”
homogeneous functions 18 234
Homogeneous functions, Euler’s theorem on 234
Hooke’s law 80
Horner’s method 679n
Hydrodynamics 416 419
Hydrostatiс pressure 593
Hyperbolic differential equation 507
Hyperbolic differential equation, difference equation for 513
Hyperbolic functions 537 591
Hypergeometric equation 165
Ideal fluid 419
Images, method of 448 462p
Implicit functions, differentiation of 230 235
Improper integrals see “Integrals”
Impulse function 759
Indefinite integral 551
Independence of path 378 393
Independence, linear 52 70 317
Independent events in probability 610 618 638
Inditial equation 161
Inertia, moment of 274
Infinite series see “Series”
Inlegrals of analytic functions 515 547 551
Inlegrals of Cauchy’s type 557
Inlegrals of complex functions 515
Inlegrals, change of variables in 270
Inlegrals, contour see “Line integrals”
Inlegrals, convergence of, absolute 755
Inlegrals, differentiation of 261 262
Inlegrals, elliptic 49 86p 118
Inlegrals, evaluation of, by fundamental theorem 9 261
Inlegrals, evaluation of, by numerical methods 717
Inlegrals, evaluation of, by residue theorem 599
Inlegrals, evaluation of, by series 117
Inlegrals, improper 118 553n 602
Inlegrals, improper, principal value of 602
Inlegrals, indefinite 551
Inlegrals, Lebesgue 774
Inlegrals, line see “Line integrals”
Inlegrals, mean-value theorem for 380
Inlegrals, multiple 270
Inlegrals, particular see “Particular integrals”
Inlegrals, probability 776
Inlegrals, Riemann 771
Inlegrals, Stieltjes 630
Inlegrals, surface 277 373
Inlegrals, transformation of 382—102
Inlegrals, volume 371
Inner product see “Scalar product”
Integral calculus, fundamental theorem of 9 261 550
Integral curve 7
Integral equations 767
Integrating factor 22
Integration, numerical 715
Interpolation 679
Interpolation formulas 696 699
Interval of convergence 139
Interval, closed 132n 772n
Interval, open 218 772n
Inverse elementary functions 539p 540p
Inversions of matrices 333 350
Inversions of order 712
Irrotational field 102
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