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Smirnov V.I. — Higher mathematics. Vol.2
Smirnov V.I. — Higher mathematics. Vol.2

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Название: Higher mathematics. Vol.2

Автор: Smirnov V.I.

Язык: en

Рубрика: Математика/Анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 630

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
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