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| Sokolnikoff I.S. — Advanced Calculus |
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| Предметный указатель |
Kelvin 128
Kepler’s equation 201 203
Knopp 173
Kummer’s test 153
Lagrange’s, expansion 198—206
Lagrange’s, expansion, identity 23
Laisant 242
Lambert’s series 172 173
Lampe 223
Laws of operation 9—12
Lebesgue 264
Legendre’s, coefficients 84 170 189 205 288
Legendre’s, transformation 119
Legendro 247
Length of curve 291 292
Limiting points 32 95 273
Limits 28 32—42 47 96
Limits of indetermination 35 36 99 100
Limits, existence of 36 39 99
Limits, maximum and minimum 34 35
Limits, theorems in 45
Liouville 492
Lipschitz’s condition 72
Logarithmic function 44 46 178 183
Logarithmic series 184
M-test 159 187
M-test for integrals 437
M-test for products 232
Maclaurin 403
MacRobert 170 201 289
Maxima and minima 211 216
Maxima and Minima of implicit functions 219
Maxima and minima, absolute 218
Mean value, integral theorems of 277 316 387
Mean value, theorem of 70 105
Mean, arithmetico-geometric 31
Mean, arithmetico-harmonic 31
mellin 255
Meray 2
meshes 310
Molk 235 237 244
Monotonic function 28
Monotonic sequence 29
Multiplication 11
Multiplication of series 169
Multipliers, undetermined 193
Neighbourhood 58 94
Nielsen 78 241 275 489 495 496 499
normal 328
Normal positive and negative directions of 357
Null sequence 28
NUMBER 1 3
Number, absolute value of 11
Number, approximations to 15
Number, correspondence of, to point 1 16
Number, decimal representation of 14
Number, irrational 1 3 6 8 15
Number, natural 3 14
Number, negative 7
Number, positive 7
Number, rational 1 3 6 8 15
Number, real 6—17
Number, zero 7
Numbers, sections of 12
Open interval 17
Open region 95 96
Oscillation of a function 56 266 267
Ostrogradsky 361
Parameter, integral as function of 302—309 411—415 426 436—444 451
Parameters, change of 330
Partial fractions, expansion of function in terms of 236 239
Peano 211 217
Po1ya 406
Point 94
Point of condensation 32 95
Point of discontinuity 273
Point of infinite discontinuity 408 412
Point, admissible 99
Point, correspondence of number and 1 16 25
Point, limiting 32 95 273
Point, singular see under “Singularity”
poisson 433
Poussin 291 411 430 436 438 446 451 463
Power 18
Power series 190—206
Power series, substitution of a power series in a 190
Power, generalised 180 183
Pringsheim 464
Products, infinite 224—236
Products, infinite for Gamma function 246
| Products, infinite for hyperbolic functions 236
Products, infinite for trigonometric functions 235
Products, infinite, convergence of see under “Convergence of products”
Products, infinite, derangement of factors in 230
Products, infinite, differentiation of 233
Quantic 210
Raabe’s test 154
Rectification of curves 291 300
Regions, sequence of decreasing 97
Reversion of series 194
Riemann’s theory of integration 264
Rodrigues 81
Rodrigues’ formula 84
Rodrigues’ formula, formula for  205
Rolle’s Theorem 68
Roots 17
Rouche 201
Schaar 488
Schlomilch 78 86 222 301 339 483 484
Schobloch 499
Schwarz’s inequality 23 289
Section 2—9 12
SEQUENCE 25 34
Sequence of decreasing regions 97
Sequence of intervals 31
Sequence, limit of 28 36
Sequence, monotonic 29
Sequence, notation for 26
Sequence, null 28
Series see under “Convergence of”
Series, binomial 185
Series, Cesaro’s theorem for divergent 164 251
Series, derangement of terms of a 151 166 175
Series, division by a 192
Series, integration of 468—475
Series, logarithmic 184
Series, multiplication of 169
Series, power see under “Power series”
Series, reversion of 194
Serret 201 202 205
Set 25
Set, bounded 26 32 99
Set, finite 25
Set, infinite 25 258
Set, limiting point of 32—34 95
Set, point of condensation of 32 95
Singularity 375 376 381
Singularity, removable 389
Stirling’s approximation 55 484
Stokes’s theorem 358
Stolz 217 430 433 463
Subtraction 10
Sums, upper and lower 259 310 342
Superposition of divisions 257
Surface, area of a curved 325
Surface, curves on a 327
Surface, element of a 329
Surface, integrals 355 358 360
Surface, normal to a 328 357
Surface, positive and negative side of a 357
Szega 406
Tait 434
Tannery 235 237 244
Tannery’s theorem 161 175
Tannery’s theorem for integrals 443
Tannery’s theorem for products 234
Taylor’s Theorem 110
Taylor’s theorem, remainder in 209 213
Tisserand 74 75 78
Todhunter 221 334
Transformation of integral 284 332 345—355 380 388 428 430
Transformation of Laplace’s equation 362
Transformation, orthogonal 354
Trigamma function 248
Trigonometric functions 176 182
Trigonometric functions, infinite products for 235
Trigonometric functions, inverse 179 183
Trigonometric functions, series of partial fractions for 236—238
Tweedie 55
Variable, continuous 1 17
Variation, limited 263 269
Variation, total 263 264
Volume, element of 343 353
Volume, measure of 324
Wallis 54
Watson 201 399
Weierstrass 2 32 159 209 247
Whittaker 201 399
Wolstenholme 476
Wronskians 91—93
Zero 7
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