|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Sokolnikoff I.S. — Advanced Calculus |
|
|
|
| Предметный указатель |
 -function, Gauss’s 247
 -function, Gauss’s 248 249 485 496
Abel 491
Abel’s, inequality 157
Abel’s, test 157 159
Abel’s, theorem 162 187
Abel’s, theorem for integrals 385 437
Addition 10
Admissible values of variable 40
Aggregate 25
Analytical continuation 133
Andoyer 201
Angle, solid 366
Approximations to numbers 15
Arc to chord, ratio of 295
Archimedes 9
Area of closed curve 299
Area of curved surface 325
Area, element of 312 314 326 329 352
Area, measure of 298
Area, sign of 358
Argand diagram 173
Asymptotic expansion for log  484
Axes, change of 329
base e 45
Bateman 143
Bell 128 328 354 371
Bernoulli’s numbers 239—241 475
Bertrand 456 466
beta function 388 389 431 462
Binet’s function  481 484
Binomial series 185
Bocher 212
Bolzano — Weierstrass theorem 32
Borchardt 50
bounds 26 56 61 62 99 102 211 258 310 342
Bromwich 2 151 153 157 159 161 165 169 187 201 213 226 238 395 443 456 463 473 485 496
Cantor 2
Cauchy 39 196 201 377 481
Cauchy’s, condensation test 155
Cauchy’s, first and second theorems 39
Cauchy’s, integral test 403
Cauchy’s, test for sequences 36
Cauchy’s, test for series 157
Cesaro 53 165
Cesaro’s theorem 164 251
Change of axes 329
Change of parameters 330
Change of variables in partial derivatives 112
Chord to arc, ratio of 295
Chrystal 2 3 12 15 19 155 180 209 217 235 238 241 244
Clausen 172
Closed interval 17
Closed region 95 96
Columns 324
Complex functions of a real variable 181 397
complex numbers 173
Condensation, point of 32 95
Continuity 2 13 17 41 58—62 97 100—102
Continuity of integral with respect to a parameter 304 415—418 440
Continuity, uniform 61 100
Continuum 17
convergence of integrals 376—386 408—414
Convergence of integrals, absolute 378 411
Convergence of integrals, tests for 381 382 385 386 391
Convergence of integrals, uniform 411
Convergence of integrals, uniform in general 413
Convergence of products 224—236
Convergence of products, absolute 227
Convergence of products, Tannery’s theorem for 234
Convergence of products, tests for 226
Convergence of products, uniform 232
Convergence of series 151—164 173—175 403
Convergence of series of complex terms 173
Convergence of series, Abel’s theorem for 162 187
Convergence of series, absolute 174
Convergence of series, conditional 153
Convergence of series, Tannery’s theorem for 161 175
Convergence of series, tests for 153—158 403
Convergence of series, uniform 158—163 187
Correspondence of number and point 1 16 25
Curve of infinite discontinuity 408
Curve on a surface 327
Curve, auxiliary 409
Curve, composite 293 299
Curve, quadrable 300
Curve, rectifiable 291 300
Curve, tangent to 295 328
Curvilinear integral 296
Darboux 235 237
Darboux’s theorem 261 311
Decimal representation 14
Dedekind 22
Dedekind’s axiom 2
Dependence of functions 142—146
Dependence of functions, linear 90—92
Derangement of a product 230
Derangement of a series 151 166 175
derivatives 63 64 66
Derivatives of  46
Derivatives of complex functions 181—183
Derivatives of determinants 88
Derivatives of implicit functions 134
Derivatives of inverse functions 68
Derivatives, change of variables in 112—120
Derivatives, higher 78—84
Derivatives, partial 103—120
Determinant, derivative of 88
Determinant, derivative of, Hadamard’s 219
Differential equations 120—122
Differentials 75—77 105—112
Differentials, higher 76 109
Differentials, total 107
Differentiation of Lagrange’s expansion 204
Differentiation of products 233
Differentiation under the integral sign 307 426 451
Digamma function 248
Dini 473
Dirichlet 492
Dirichlet’s, formulae 334
Dirichlet’s, test 158 160 187
Dirichlet’s, test for integrals 386 438
Dirichlet’s, theorem on derangement of series 151
Discontinuity 62
Discontinuity of integrand 273 303 315
Discontinuity of the first or second kind 63
Discontinuity, admissible 273 317
Discontinuity, curve of infinite 408 412
Discontinuity, line of 303
Discontinuity, normal 304
Discontinuity, planes of 344
Discontinuity, point of 273
Discontinuity, point of infinite 408 412
Discontinuity, removable 62
Division 11
Division by a series 192
Division of area of integration 312
Division of interval 257
Division, consecutive 257
D’Alembert’s test 157
Element of sequence 25
Element of set 25
Element of surface 329
Element of volume 343 353
Elimination of functions 120—122
Elliptic coordinates 371
Equality 7
Ermakoffs tests 406
Euclid 9
Eudoxus 9
| Euler 177 235 242
Euler’s, constant 51 246 404 478
Euler’s, numbers 244
Existence theorems 131 134 139 191 192 207
Exponent of a power 18
Exponential function 42 46 175 182
Exponential function, periodicity of 177
Extension of range of definition of function 49 400
Factorisation of function of two variables 209
Fluctuation of function 263
Forms, algebraic 209—213
Forsyth 119 122
Fourier’s double integral 464
Frobenius 165
Frullani’s integral 395
Functions of functions 66 102
Functions of several variables 94—122 130—147
Functions with limited variation 263 269 Beta Gamma Logarithmic Hyperbolic Hypergeometric and
Functions, arbitrary 121
Functions, bounded 29 (see also under “Bounds”)
Functions, complex 181—186 397
Functions, continuous 56 208
Functions, dependent 90—92 142—146
Functions, difierentiable 63 64
Functions, discontinuous 62 63
Functions, expansion in series of 190
Functions, extension of range of definition of 49
Functions, factorisation of implicit 209
Functions, implicit 130—142 206—209 219 353
Functions, independent 90 142
Functions, integrable 265—276 314—317 344 378 379 382—386
Functions, inverse 44 67 142
Functions, limits of 40
Functions, monotonic 28 263 269
Functions, oscillation of 56
Functions, region of definition of 94 95
Functions, strictly decreasing 29
Functions, strictly increasing 29
Functions, values of 41 97
Gamma function 245—254 398
Gamma function, as an integral 398
Gamma function, asymptotic expansion for logarithm of 484
Gamma function, Gauss’s multiplication formula for 252 483 499
Gamma function, integral for logarithm of 480 487
Gamma function, integrals expressible in terms of 489—495
Gamma function, minimum value of 488
Gamma function, product formula for 246
Gauss 31
Gauss’s, -function 247
Gauss’s,  -function 248 249 485 496
Gauss’s, multiplication formula for  252 483 499
Gauss’s, test 154
Godefroy 489
Goursat 87 131 143 201 263 264
Green’s Theorem 335
Green’s theorem, general theorem 360
Hadamard’s determinant 219
Halphen 86
Hardy 2 171 394 395 397 455 473
Heath 9
hermite 72 201 203 488
hessian 147
Hilton 213 467
Hobson 2 6 9 12 64 180 217 238 323 408 411
Hyperbolic functions 178 236 237 239
Hypergeometric function 156 251 477 478
Index of a power 18
Inequalities 19 47
Inequality 8
Infinitesimals 75 105
Integrability of a function, condition of 265 314
Integrable functions 265—276 314—317
Integral of complex function 181 183 397
Integral, as function of a parameter 302—309 411—415 426 436—444 451
Integral, as measure of an area 298
Integral, curvilinear 296 308 335 359
Integral, definite 264 265 267
Integral, definite, as a function of its limits 279
Integral, definite, change of variable in see under “Transformation of integral”
Integral, definite, continuity of 279
Integral, definite, continuity with respect to a parameter of 304
Integral, definite, properties of 276
Integral, differentiation of 279 307 426 451
Integral, double 310—323
Integral, double, change of variables in 332 345
Integral, double, reduction to repeated integrals of 317
Integral, finite 375
Integral, Fourier’s double 464
Integral, generalised 375
Integral, improper 375—391
Integral, improper double 408—430 440 445 463
Integral, improper double with infinite limits 445 463
Integral, improper double, absolute convergence of 411
Integral, improper double, change of variables in 430
Integral, improper double, continuity of 416 440
Integral, improper double, evaluation of 429
Integral, improper with range finite 376
Integral, improper with range infinite 378 436
Integral, improper, Abel’s theorem for 385
Integral, improper, absolute convergence of 378
Integral, improper, as function of its limits 384
Integral, improper, as limit of a sum 401
Integral, improper, change of values of integrand in 380
Integral, improper, change of variable in 380 388 428
Integral, improper, comparison test for 391
Integral, improper, continuity with respect to a parameter of 415 440
Integral, improper, convergence at infinity of 381
Integral, improper, convergence of 376
Integral, improper, convergence- at a singular point of 381
Integral, improper, differentiation of 426 451
Integral, improper, Dirichlet’s theorem for 386
Integral, improper, limit with respect to a parameter of 441 443 444
Integral, improper, mean value theorems for 387
Integral, improper, oscillating 378
Integral, improper, principal values of 377 378
Integral, improper, singular integrals at singular points of 380
Integral, improper, singular points of 375
Integral, improper, tests for convergence of 381 382
Integral, improper, transformation to proper integral of 380
Integral, improper, uniform convergence in general of 413 436
Integral, improper, uniform convergence of 411 436
Integral, indefinite 280
Integral, infinite 375
Integral, integration of 308
Integral, multiple 342
Integral, multiple, improper 430
Integral, multiple, standard form for 349
Integral, proper 375
Integral, proper double 408
Integral, quadruple 345
Integral, repeated 317—323 344 416—426 445—449 458—463
Integral, repeated with one limit infinite 445
Integral, repeated with two limits infinite 458
Integral, surface 355 358 360
Integral, triple 343
Integral, volume 343 353 360
Integrals, upper and lower 265 312 343
Integration by parts 284
Integration of series 468—475
Integration, change of order of 308 318 418—426
Integration, Riemann’s theory of 264
interval 17
Interval, closed 17
Interval, division of 257
Interval, method of the decreasing 32
Interval, open 17
inversion 44 142 179
jacobi 81
Jacobian 108 136—147 350—354
JORDAN 217 291 292
|
|
|
| Реклама |
|
|
|
|
|
О проекте