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| Demidovich B. (ed.) — Problems in mathematical analysis |
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| Предметный указатель |
Removable discontinuity 37
Right horizontal asymptote 93
Right inclined asymptote 93
Right-hand derivative 44
Rolle's theorem 75
Root multiplicities 121
Rose, four-leafed 487
Rose, three-leafed 20 487
Rotation (of a vector field) 288
Rule of proportionate parts 376
Rule, l'Hospital — Bernoulli 78—82
Rule, Leibniz 67 269
Runge principle 383 386
Runge — Kutta method 385—387 390
Safety parabola 234
Scalar field 288
Scheme, twelve-ordinate 393—395
Second curvature 243
Second derivative 66
Second differential 198
Second partial derivative 197
Second-order differential 72
Segment of a straight line 20
Segment of the normal 61
Segment of the polar normal 61
Segment of the polar tangent 61
Segment of the tangent 61
Semicircle 20
Semicubical parabola 18 20 234 481
Series with complex terms 297
Series, absolutely convergent 296 297
Series, conditionally (not absolutely) convergent 296
Series, convergent 293
Series, Dirichlet 295 296
Series, divergent 293 294
Series, Fourier 318 319
Series, functional 304
Series, harmonic 294 296 297
Series, incomplete Fourier 318 319
Series, MacLaurin's 311 313
Series, number series 293
Series, operations on 297
Series, power 305
Series, Taylor's 311 313
Serpentine, Newton's 18
Simpson's Formula 382—384
Sine curve 481
Single-valued function 11
Singular integral 337
Singular point 230
Slope (of a tangent) 43
Smallest value 225 227
Solenoidal vector field 289
Solution (of an equation) 322
Solution (of an equation), general 323 359
Solution (of an equation), particular 339
Spiral of Archimedes 20 65 66 105 487
Spiral, hyperbolic 20 105 487
Spiral, logarithmic 20 21 105 106 487
Static moment 168
Stationary point 196 222 225
Stationary scalar or vector field 288
Stokes' formula 285 286 289
Straight line 17 20
Strophoid 157 232 234 486
Subnormal 61
Subnormal, polar 61
Substitutions, hyperbolic 114 116 133
Substitutions, trigonometric 114 115 133
Subtangent 61
Subtangent, polar 61
Successive approximation 377 385
Successive approximation, method of 384 385 389
Sufficient conditions (for an extremum) 222
Sum of a series 293 304
Sum of two convergent series 298
Sum, integral 138
Sum, partial 293
Superposition of solutions, principle of 353
Surface integral of the first type 284
| Surface integral of the second type 284
Surface integrals 284—286
Surfaces, level 288
Surfaces, orthogonal 219
Table interval 372
Table of standard integrals 107
Table, diagonal table 389
Tabular differentiation 46
Tacnode 230
Tangency, point of 217
Tangent 238
Tangent curve 481
Tangent plane 217
Tangent plane, equation of 218
Tangents, method of 377
Taylor's formula 77 220
Taylor's series 311 313
Term, general 294
Term, remainder 311
Test, Cauchy's 293 295
Test, Cauchy's integral 295
Test, comparison 143 293 294
Test, d'Alembert's 295
Test, Leibniz 296 297
Test, Weierstrass' 306
Theorem, Cauchy's 75 326
Theorem, Dirichlet's 318
Theorem, Lagrange's 75
Theorem, Ostrogradsky — Gauss 291
Theorem, Rolle's 75
Theorems, Guldin's 171
Theorems, mean-value 75 150
Theory field 288—292
Three-leafed rose 20 487
Torsion 243
Tractrix 161
Trajectories, orthogonal 328
Transcendental functions, integration of 135
Transformation, Laplace 271
Trapezoidal formula 382
Trident of Newton 18
Trigonometric functions 48
Trigonometric functions, integrating 128 129
Trigonometric substitutions 114 115 133
Trihedron, natural 238
Trinomial, quadratic 118 119 123
Triple integral 262
Triple integral in rectangular coordinates 262
Triple integral, applications of 265 268
Triple integral, change of variables in 263
Triple integral, computing volumes by means of 268
Triple integral, evaluating a 265
Trochoid 157
Twelve-ordinate scheme 393—395
Undetermined coefficients, method of 121 351
Uniform convergence 306
Value, greatest 85 225 227
Value, least 85
Value, mean (of a function) 151 252
Value, smallest 225 227
Variable, dependent 11
Variable, independent 11
Variables separable an equation with 327 328
Variation of parameters 332 349 352
Vector field 288
Vector function 235
Vector lines 288
Vector of binormal 238
Vector of principal normal 238
Vector of tangent line 238
Vector, acceleration 236
Vector, velocity 236
Velocity vector 236
Vertex of a curve 104
Vertical asymptote 93
Vertices of a curve 104
Volume of a cylindroid 258
Volume of solids 161—166
Weierstrass' test 306
Witch of Agnesi 18 156 480
Work of a force 174 276 277
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