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| Sokolnikoff I.S. — Mathematics of Physics and Modern Engineering |
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| Предметный указатель |
 172 536 581
 173 536
 see “Bessel’s functions”
 see “Bessel’s functions”
 510 692
 370
 387 407
Abel’s theorem on differential equations 54p
Abel’s theorem on power series 142
Absolute convergence of integrals 755
Absolute convergence of series 127 170
Absolute value of complex numbers 168 528
Acceleration, normal 313
Acceleration, tangential 313
Acceleration, vector 302p 313
Acceleration, vector, in cylindrical coordinates 367p
Adams’ method 723 728
Addition of complex numbers 166 529
Addition of matrices 327
Addition of series 117
Addition of vectors 288 317
Addition, parallelogram law of 288 529
Adiabatic expansion 50p
Algebraic equations 677
Algebraic equations, solution of, by graphical methods 678
Algebraic equations, solution of, by iterative methods 679
Algebraic equations, systems of linear 350 687 689 719
Alternating series 128
Amplitude of simple harmonic motion 44
Amplitude of waves 428
Analytic functions 540
Analytic functions, branch points of 570
Analytic functions, Cauchy’s formula for 555
Analytic functions, Cauchy’s theorem for 547
Analytic functions, differentiation of 511 557
Analytic functions, essential singular points of 570 574
Analytic functions, geoimetric representation of 575
Analytic functions, integrals of 515 547 551
Analytic functions, Laurent’s expansion for 565
Analytic functions, mapping by 575—591
Analytic functions, maximum modulus theorem for 558 561
Analytic functions, poles of 570
Analytic functions, residue theorem for 573
Analytic functions, residues of 570
Analytic functions, singular points of 543 569
Analytic functions, Taylor’s series for 561
Angle, phase 44 528
Angle, solid 399p
Angular velocity 302 399p
Antenna, radiation from 486
Arc length 301
Arc length in curvilinear coordinates 362
Arc length of an ellipse 147
Argand’s diagram 528
Argument of a complex number 528
Arithmetic means 667
Asymptotic equality 12 123
Atmospheric pressure 50 (see also “Pressure”)
Attraction of a cone 277p
Attraction of a cylinder 277p
Attraction of a sphere 47 277p 410
Attraction, Coulomb’s law of 408n
Attraction, Newton’s law of 16
Augmented matrix 750
Average, arithmetic 667
Average-value theorem 498
Base or coordinate vectors 319
Base or coordinate vectors in curvilinear coordinates 363
Base or coordinate vectors in cylindrical coordinates 367p
Base or coordinate vectors in spherical coordinates 367p
Base or coordinate vectors, orthonormal 321
Base or coordinate vectors, transformation of 337 367p
Basis 319
Beams on elastic foundations 86p 94p
Beams, bending of 15
Beams, buckling of 95p
Beams, cantilever 16
Beams, vibration of 435p
Bending moment 16 435
Bernoulli — Euler law 10
Bernoulli’s differential equation 27
Bessel’s differential equation 159
Bessel’s functions 162 198 480
Bessel’s functions, asymptotic formulas for 199p
Bessel’s functions, expansion in series of 481
Bessel’s functions, generating function for 166р
Bessel’s functions, orthogonality of 198
Bessel’s functions, zeros of 198
Bessel’s inequality 202
beta function 149 765
Biharmonic equation 430p
Bilinear forms 349
Bilinear transformation 577p
Binomial distribution 639
Binomial distribution, generating function for 640p
Binomial frequency function 639
Binomial law of probability 639
Binomial law of probability, Laplace’s approximation to 647
Binomial law of probability, normal approximation to 647
Binomial theorem 155
Binormal 312
Boltzmann constant 633
Boundary-value problems 91 442 730
Bounds for Fourier coefficients 211
Branch points 570
Buffon’s needle problem 637
Cable, flow of electricity in 514
Cable, hanging under gravity 40 454
Cable, oscillations of 445 454
Cable, supporting roadway 42p
Calculus of variations 264
Calculus of variations, isoperimetric problems 269
Calculus of variations, problems with constraints 269
Cantilever beam 16
Cartesian reference frames 321
Catenary 41
Cauchy — Riemann equations 413
Cauchy — Schwarz inequality 322
Cauchy’s convergence criterion 115
Cauchy’s differential equation 78
Cauchy’s inequality 322
Cauchy’s integral formula 555
Cauchy’s integral test 120
Cauchy’s integral theorem 547
Cauchy’s principal value of an integral 602
Center of gravity 275 281
Center of mass 44 303
Center of mass, motion of 44 304
Chain rule 228
Chain under gravity 40
Change of variables in functions 237
Change of variables in integrals 270
Channel, flow from 594
Chaplygin’s method 37
Characteristic equation 54 67 521 733
Characteristic equation for systems of linear differential equations 100 106p 733
Characteristic equation of a matrix 344
Characteristic frequencies 477 479p 481 482p
Characteristic functions 732
Characteristic values 344 507p 732
Characteristic vectors 344
Characteristics 440 508 517
Characteristics, discontinuities on 519
Chemical combinations 14
Chemical reactions 15
Circle of convergence 170 562
Circulation 397 591
Clairaut’s equation 27p
Cofactors 741
Column, axially loaded 86p 90
| Column, Euler’s critical load for 92
Combinations 611
Combinatory analysis 611
Comparison tests for inlegrals 755n
Comparison tests for series 122 125 131
Complementarу function 59
Complex function 534
Complex function, continuitv of 5—10
Complex function, differentiation of 511
Complex function, integration of 543
complex numbers 166 527
Complex numbers, absolute value of 168 528
Complex numbers, addition of 166 529
Complex numbers, argument of, principal 528
Complex numbers, conjugate 529
Complex numbers, modulus of 528
Complex numbers, operations on 528
Complex numbers, phase angle of 528
Complex numbers, polar form of 528
Complex numbers, roots of 531
Complex potential 587
Complex roots of unity 532
Complex variable, elementary functions of 534
Complex-variable theory 523—601
Components of a vector 291 317 321
Composite functions 230
Compound probability 617 635
Condenser discharge 81 84
Conductivity, thermal 115 455
Conformal mapping 583 598
Conformal mapping, examples of 575—595
Conformal mapping, invariance of harmonic functions under 585
Conformal mapping, Riemann’s theorem on 586
Conformal mapping, Schwarz — Christoffel formula for 599
Conjugate complex numbers 529
Conjugate harmonic functions 560 588
Conjugate matrix 343
Conservation of energy 43
Conservation of matter 417
Conservation of momentum 44
Conservative force fields 108
Constraints in calculus of variations 269
Continuity 218
Continuity of complex functions 540
Continuity of scalar functions 368
Continuity of vector functions 299 368
Continuity, equation of 112 417
Continuity, piecewise 755
Contour integrals see “Line integrals”
Convergence of series see “Series”
Convergence, circle of 170 562
Convergence, interval of 139
Convergence, radius 139 170 562
Convergence, uniform 132
Convolution 188
Convolution theorem 188 762
Coordinate lines 272 359
Coordinate surfaces 359
Coordinate vectors 319
Coordinate, affine 366
Coordinate, curvilinear 357
Coordinate, cylindrical see “Cylindrical coordinates”
Coordinate, divergence in 106
Coordinate, gradient in 107
Coordinate, orthogonal 363
Coordinate, parabolic 108p
Coordinate, spherical 360 367p
Coordinate, volume in 361
Correlation coefficient 666
Coulomb’s law 108n 167
Couple 305
Covariance 661
Cramer’s Rule 326 719
Cross product 291
Crout’s reduction 687n
Curl 396
Curl in caitesian coordinates 398
Curl in curvilinear coordinates 406
Curl, relation to rotation 399p
Current flow 416
Current flow in cables 514
Current flow in electrical circuits 81 87 100 761p 768p
Curvature 150 311
Curve fitting by finite differences 694
Curve fitting by graphical means 701
Curve fitting by least squares 702
Curve fitting by trigonometric functions 711
Curve integral 7
Curve of minimum descent 269p 767
Curve on a surface 309
Curve, elastic 16 86p
Curve, Frenet’s formulas for 311
Curve, length of 301
Curve, minimizing 265
Curve, motion on 301 313
Curve, normal to 311
Curve, piecewise of sectionally smooth 372
Curve, pursuit 33
Curve, trihedral associated with 312
Curvilinear coordinates see “Coordinates”
Cycloid, motion on 46p 269p 767
Cylindrical coordinates 359
Cylindrical coordinates, acceleration components in 367p
Cylindrical coordinates, base vectors in 367p
Cylindrical coordinates, velocity components in 367p
Cylindrical coordinates, volume element in 365
D 57
Damped oscillations 449
Damping, viscous 82 449
De Moivre’s Formula 530
Deformation of contours 549
Del, see “Gradient”
Delmite integrals see “Integrals”
Dependence, linear 52 70 317
Derivative, directional 243 253 369
Derivative, normal 244 253 369
Derivative, partial 219
Determinante 325 741—753
Determinants, cofactors of 741
Determinants, differentiation of 743
Determinants, expansion of 326 741
Determinants, minors of 741
Determinants, multiplication of 325 745
Determinants, solution of equations by 326 748
Determinants, Wronskian 52 54p 71
Difference equations 510 734
Difference equations, Dirichlet’s problem for 511
Difference equations, elliptic 511 518
Difference equations, hyperbolic 513 518
Difference equations, parabolic 512 518
Difference operators 510 692
Differences, backward 692
Differences, finite, method of 734
Differences, forward 691
Differentiability 226
Differential 223 310
Differential equations, elliptic 505 511 518
Differential equations, Euler’s 78 267
Differential equations, exact 20
Differential equations, hyperbolic 507
Differential equations, Lagrange’s 26
Differential equations, ordinary see “Ordinary differential equations”
Differential equations, parabolic 506 512
Differential equations, partial see “Partial differential equations”
Differential equations, systems of 95 733
Differential form, quadratic 362
Differential of arc length 362
Differential of volume 364
Differential operators 57 430p
Differential, approximations by 226 311
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