|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Smirnov V.I. — Higher mathematics. Vol.2 |
|
|
|
| Предметный указатель |
Abel's problem 244 268
Abelian summability of series 585
Absolute convergence of improper integrals 256 270 272
Absorption, of waves 546
Angular velocity, instantaneous 309 324
Approximation of function 444
Approximation of period function 446
Area, definition of 282
Area, evaluated by curvilinear integral 214
Area, exterior and interior 282
Area, surface 191
Bending of beams 49
Bernoulli equation 9
Bernoulli numbers 411
Bessel equation 136
Bessel functions 137—139
Bessel inequality 417 420
binomial 359 362
Boundary of domain 280
Boundary of set 280
Buniakowski's inequality 454
Cauchy test for absolute convergence 256 258
Cauchy — Riemann equation 232
Change of variables in double integral 176 239
Change of variables in n-ple integral 295
Change of variables in triple integral 189
Characteristic equation 85 90
Characteristic(s) 486
Circulation 227 228
Clairaut's equation 28
Closed set 279
Closed system of functions 451—455
Closure, equation of 409 421 451
Collinear plane flow of fluid 155
Completeness, of system of functions 423
Connectivity, of domain 228
Continuity, equation of 326
Convergence of Fourier series, nature of 455
Coordinate lines 174 337 368
Coordinate surfaces 337
Coplanarity of vectors 307
Cotangent expansion in partial fractions 409
Curl, of vector 318
Curvature of curve 350 358
Curvature, centre of 351
Curvature, Gaussian 380 386
Curvature, lines of 380
Curvature, mean 380 388
Curvature, of line on surface 373
Curvature, radius of 350 358
Curvature, vector 358
Curve, Gaussian 380 386
Curve, plane 358
Curve, simple 286
Curve, spatial 358
Curvilinear coordinates 174 188 337
Cyclical constants of function 228—230
Cylindrical coordinates 182
Cylindrical waves 510
d'Alembert's solution of vibration of string 480—483
Darboux's theorem 289—290
Derivative, local 343
Derivative, particle 343
Developable surface 394
Differential equation, Bernoulli 9
Differential equation, Bessel 136
Differential equation, Clairaut 28
Differential equation, Euler 119
Differential equation, first order ordinary, system of 58—61 66
Differential equation, Lagrange 30
Differential equation, linear, first order 9
Differential equation, linear, homogeneous 5
Differential equation, linear, homogeneous second order 77 129
Differential equation, linear, homogeneous second order, with constant coefficients 84 86
Differential equation, linear, non-homogeneous second order 80
Differential equation, linear, non-homogeneous second order, with constant coefficients 86—88
Differential equation, linear, of higher order 82
Differential equation, linear, of higher order, with constant coefficients 90 113 116
Differential equation, linear, partial 68
Differential equation, linear, partial, with constant coefficients 121
Differential equation, ordinary 1
Differential equation, partial 1
Differential equation, reducible to Bessel equation 139
Differential equation, Riccati 15
Differential equation, to lower order 54
Differential equation, total 233 238
Differential equation, variables separable 2
Differentiation, in case of variable field 343—348
Differentiation, of integral with respect to parameter 247
Differentiation, of vectors 310
Directed element of surface 321
Direction of circuit round curve 217 221
Dirichlet conditions 402
Dirichlet integral 438—442
Dirichlet problem, exterior 569
Dirichlet problem, interior 569 577
Dirichlet problem, solution, for circle 578—586
Dirichlet problem, solution, for sphere 586—590
Dirichlet theorem in Fourier series 402 442
Displacement vector 324
Distance between sets 281
Divergence 316
Domain 279
Domain, measurable 284
Dupin's theorem 383
Elementary area in curvilinear coordinates 175
Elementary area in polar coordinates 173
Elementary area in rectangular coordinates 171
Elementary area of surface 193
Elementary area, directed 321
Elementary volume in curvilinear coordinates 188
Elementary volume in cylindrical coordinates 184
Elementary volume in spherical coordinates 186
Elliptic coordinates 385
Elliptic coordinates, point of surface 375
Envelope of family of curves 32
Envelope of family of lines in space 393
Envelope of family of surfaces 391
Envelope, normal 352
Error, root mean square 413
Euler differential equation 119
Euler form of hydrodynamical equation 330
Euler formula 378
Euler number 411
Euler problem of “longitudinal bending” 106
Euler — Cauchy method of approximate construction 19
Even continuation 407
Even function 403
Evolute 351
Flow, field of 315
Flow, steady 211 231 234
Forced vibrations of string 498—505
Forced vibrations of system, one degree of freedom 97—101
Fourier integrals 464 470—472 534
Fourier method for Dirichlet problem, mathematical physics 579
Fourier method for membrane vibration 520 524
Fourier method for oscillatory current 552
Fourier method for thermal vibration in sphere 618
Fourier method for vibration of rod 561
Fourier method for vibration of rod, finite 492—493
Fourier method, heat propagation in finite rod 615
Fourier method, heat propagation in infinite rod 604
Fourier series 397
Fourier series, coefficients of 401 412
Fourier series, generalized 419
Fourier series, generalized, coefficients of 419
Fourier series, in complex form 472
Fourier series, multiple 473
Frenet's formula 362
Fresnel integral 262
| Fundamental vectors see Unit vectors
Gauss differential form, first 370
Gauss differential form, second 371
Gaussian curvature of surface 380 386
General integral of differential equation, first oder 22
General integral of differential equation, higher order 40
General integral of differential equation, solution of differential equation, first order 71
General integral of differential equation, solution of differential equation, of system of 59
Generalized sum of divergent series 585
Geodesic 365
Geometric interpretation, differentials equation in 239
Geometric interpretation, of first order equations 71
Gradient of scalar field 312
Graphical integration of differential equations 43
Gravitational field 274 314
Green's formula 216 570—572
Green's function 590—592
Harmonic analysis, practical 423
Harmonic functions 568 574
Harmonic oscillations 95
Heat flow vector 315
Helix 364
Huygen's principle 488
Hydrodynamic equations for ideal fluid 329
Hyperbolic point of surface 375—376
Incompressibility, condition for 231 328
Independence of line integral from path 221 229
Indical equation 134
Indicatrix (Dupin's) 376
Integrable functions 290—292
Integral, curve 2
Integral, depending on parameter 242—255
Integral, Dirichlet 438—442
Integral, double 168—177 290
Integral, equation, Fourier 470
Integral, Fourier 464—475
Integral, general, of differential equation, first order 2 23
Integral, general, of differential equation, higher order 40
Integral, general, of differential equation, system of 59
Integral, improper, multiple 269
Integral, improper, multiple, of discontinuous function 255
Integral, improper, multiple, with infinite limits 258
Integral, iterated 166
Integral, Laplace 243
Integral, line 205—210
Integral, multiple 295
Integral, non-absolutely convergent 259
Integral, Poisson 582
Integral, surface 195
Integral, triple 178—182
Integral, uniformly convergent 262
Integrating factor 233 239
Integration with aid of power series 128—136
Integration with respect to parameter 242
Interior point of set 279
Involute 355
Isoclines 26
Isogonal trajectories 37
Isolated point of set 280
Jacobian 176 189 240 295
Kirchhoff's formula 600
Lagrange equation 30
Lagrange identity 305
Lagrange method of variation, arbitrary constants, for first order linear equations 10
Lagrange method of variation, arbitrary constants, for higher order linear equations 83
Lagrange method of variation, arbitrary constants, for second order linear equations 81
Lamellar field 319
Laplace equation 276 329 333 337 568—594
Laplace operator 323
Laplace operator in cylindrical coordinates 342
Laplace operator in orthogonal coordinates 337
Laplace operator in spherical coordinates 341
Limit-point of set 279 281
Line integral 205—210
Linear differential equation, first order 9
Linear differential equation, higher order 82
Linear differential equation, higher order with constant coefficients 90 113—117
Linear differential equation, independence of solutions 82
Linear differential equation, partial 68
Linear differential equation, second order 77 80
Linear differential equation, with constant coefficients 84 86—88
Lipschitz condition 150
Logarithmic decrement of damping 543
Maxwell's equations 334
Mean square error 414
Mean value theorem for multiple integrals 191
Mean value theorem for multiple integrals, second 434
Measurable set 284
Measure, theory of, for n-dimensional space 288
Measure, theory of, for plane 284
Membranes, vibration of 519—531
Meusnier's theorem 374
Moment of vector 309 310
Moments of system of points 200—202
Multiply connected domain 226
Natural, equation of curve 356
Neumann's problem 570 577
Normal, principal 358
Normal, to surface 369
Order of differential equation 1
Order of differential equation, lowering 54
Orthogonal coordinates 337
Orthogonal trajectories 37
Orthogonality of trigonometric functions 399
Oscillation, of current in circuit 550—556
Osculating plane 363
Ostrogradski's formula 195
Parabolic point of surface 375
Parallel curves 356
Plato's problem 389
Point, of set, isolated 280
Point, of set, limit 280
Poisson equation 278 594
Poisson formula 505
Poisson integral 582
Potential field 319
Potential field of distributed mass 275 593—596
Potential, of velocity of flow 232 329
Potential, retarded 616
Potential, simple layer 279
Principal directions 379—380
Principal radii of curvature 379—380
Propagation, wave 483 509 511
Pseudo-scalar 307
Radius of curvature 350 358
Radius of torsion 359
Reflection of wave displacement in string 492
Reflection of wave excited in circuit 543
Resonance 101 502
Riccati's equation 15
Right-handed system of axes 304
Rod, propagation of heat in 604
Rod, strength of on compression 106
Rod, vibration of 559
Rodrigues' formula 382
Rotating shaft 108
Rotation of rigid body 308
scalar 298
Scalar field 312
Scalar product 302
Second mean value theorem 434
Series, Fourier 397
Series, Fourier, generalized 419
Set, boundary 280
Set, bounded 280
Set, closed 279
Set, complementary 280
Set, derived 280
Set, diameter of 282
Set, open 279
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте