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| Авторизация |
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| Поиск по указателям |
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| Demidovich B. (ed.) — Problems in mathematical analysis |
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| Предметный указатель |
Functions, transcendental, integration of 135
Functions, trigonometric 48
Functions, trigonometric, integrating 128 129
Fundamental system of solutions 349
Gamma-function 146 150
Gaussian curve 92
General integral 322
General solution 359
General solution (of an equation) 323
General term 294
Generalized antiderivative 143
Generalized polar coordinates 255
Geometric progression 293 294
Gradient of a field 288
Gradient of a function 194 195
Graph of a function 12
Greatest value 85 225 227
Green's formula 276 281 282
Guldin's theorems 171
Hamiltonian operator 288
Harmonic series 294 296 297
Higher-order differential 198
Higher-order differential equations 345
Higher-order partial derivative 197
Hodograph of a vector 235
Homogeneous equations 330 351 356
Homogeneous linear differential equation 332 349
Hyperbola 17 18 20 485
Hyperbola, rectangular 480
Hyperbolic functions 49 484
Hyperbolic functions, integration of 133
Hyperbolic spiral 20 105 487
Hyperbolic substitutions 114 116 133
Hypocycloid 283 486
Implicit function 12
Improper integral, convergent 270
Improper integral, divergent 270
Improper multiple integrals 269 270
Incomplete Fourier series 318 319
Increasing function 83
Increment of a function 42
Increment of an argument 42
Independent variable 11
Indeterminate forms, evaluating 78 79
Infinite discontinuities 38
Infinitely large quantities 33
Infinitely small quantities 33
Infinites 33
Infinitesimals 33
Infinitesimals of higher order 33
Infinitesimals of order n 33
Infinitesimals of the same order 33
Inflection, points of 91
inhomogeneous equation 349 351 356
Inhomogeneous linear differential equation 349
Initial conditions 323 363
integral 322
Integral curve 322
Integral sum 138
Integral, convergent improper 143
Integral, definite 138
Integral, divergent improper 143
Integral, double 246
Integral, Euler 146
Integral, Euler — Poisson 272
Integral, general 322
Integral, improper multiple 269 270
Integral, line 273—278
Integral, particular 322
Integral, probability 144
Integral, singular 337
Integral, surface 284—286
Integral, triple 262
Integrating factor 335
Integration by parts 116 117 149
Integration by substitution 113
Integration of differential equation by means of power series 361 362
Integration of functions, numerical 382 383
Integration of ordinary differential equation, numerical 384—393
Integration of total differentials 202—204
Integration of transcendental functions 135
Integration under the differential sign 109
Integration, basic rules of 107
Integration, direct 107
Integration, path of 273 274 280
Integration, region of 246—248
Interpolation formula, Lagrange's 374
Interpolation formula, Newton's 372
Interpolation of functions 372—374
Interpolation, inverse 373
Interpolation, linear 13 372
Interpolation, quadratic 372
Interval of calculations 382
Interval of convergence 305
Interval of monotonicity 83
Interval, closed 11
Interval, open 11
Interval, table interval 372
Inverse circular functions 48
Inverse functions 12
Inverse hyperbolic functions 49
Inverse interpolation 373
Inverse trigonometric functions 482 483
Involute of a circle 20 106 486
Involute of a curve 104
Isoclines 325
Isolated point 230
Iterative method 377 378 380
Jacobian 253 264
kinetic energy 174
L'Hospital — Bernoulli rule 78—82
Lagrange's equation 339
Lagrange's form 311
Lagrange's formula 145
Lagrange's function 223 224
Lagrange's interpolation formula 374
Lagrange's theorem 75
Lamina, coordinates of the centre of gravity of a 261
Lamina, mass and static moments of a 260
Lamina, moments of inertia of a 261
Laplace equation 289 291
Laplace transformation 271
Laplacian operator 289
Least value 85
Left horizontal asymptote 94
Left inclined asymptote 94
Left-hand derivative 44
Leibniz rule 67 269
Leibniz test 296 297
Lemniscate 20 105 232
Lemniscate, Bernoulli's 155 486
Level surfaces 288
Limacon, Pascal's 158
Limit of a function 22
Limit of a sequence 22
Limit on the left 22
Limit on the right 22
Limiting absolute error 367
Limiting relative error 367
Limits, one-sided 22
Line integral of the first type 273 274 277 278
Line integral of the second type 274 275 278—281
Line integral, application of 276 283
Line, straight 17 20
Linear differential equations 349 351
Linear equation 332
Linear interpolation 372
Linear interpolation of a function 13
Linearly dependent functions 349
Linearly independent functions 349
| Lines, flow 288
Lines, force 288
Lines, vector 288
Lipschitz condition 385
Logarithmic curve 484
Logarithmic derivative 55
Logarithmic functions 49
Logarithmic spiral 20 21 105 106 487
Maclaurin's formula 77 220
Maclaurin's series 311 313
Maximum of a function 84 222
Mean rate of change 42
Mean value of a function 151
Mean-value theorems 75 150
Method of differentials 343
Method of elimination 359
Method of successive approximation 384 385 389
Method of tangents 377
Method of undetermined coefficients 121 351
Method of variation of parameters 332 349 352
Method, Adams' 389 390 392
Method, chord method 376
Method, Euler's broken-line 326
Method, iterative 377 378 380
Method, Milne's 386 387 390
Method, Newton's 377 379
Method, Ostrogradsky 123 125
Method, Picard's 384 385
Method, reduction 123
Method, Runge — Kutta 385—387 390
Minimum of a function 84 222
Minimum point 84
Mixed partial derivative 197
Moment of inertia 169
Moment, static 168
Monotonicity, intervals of 83
Multiple-valued function 11
Multiplicities, root 121
nabla 288
Napier's number 28
Natural trihedron 238
Necessary condition for an extremum 222
Necessary condition for convergence 293
Newton — Leibniz formula 140 141 275
Newton's interpolation formula 372
Newton's method 377 379
Newton's serpentine 18
Newton, trident of 18
Niele's parabola 18 234 481
Node 230
Nonstationary scalar or vector field 288
normal 217
Normal plane 238
Normal to a curve 60
Normal, equations of 218
Normal, principal 238
nth derivative 67
Number series 293
Number, Napier's 28
Number, real 11
Numerical integration of functions 382 383
Numerical integration of ordinary differential equations 384—393
One-sided derivatives 43
One-sided limits 22
Open interval 11
Operator, Hamiltonian 288
Operator, Laplacian 289
Order of smallness 35
Orthagonal surfaces 219
Orthagonal trajectories 328
Osculating circle 103
Osculating plane 238
Ostrogradsky method 123 125
Ostrogradsky — Gauss formula 286—288
Ostrogradsky — Gauss theorem 291
parabola 17 20 104 105 480 485
Parabola, cubic 17 105 234
Parabola, Niele's 18 234 481
Parabola, safety 234
Parabola, semicubical 18 20 234 481
Parabolic formula 382
Parameters, variation of 332 349 352
Parametric representation of a function 207
Partial derivative, "mixed" 197
Partial derivative, hirheg-order 197
Partial derivative, second 197
Partial sum 293
Particular integral 322
Particular solution 339
Pascal's limacon 158
Path of integration 273 274 280
Period of a function 14
Periodic function 14
Picard's method 384 385
Plane, normal 238
Plane, osculating 238
Plane, rectifying 238
Plane, tangent 217
Point of discontinuity 37
Point of inflection 91
Point of tangency 217
Point, bending 84
Point, critical (of the second kind) 92
Point, double 230
Point, extremal 84
Point, isolated 230
Point, maximum 84
Point, minimum 84
Point, singular 230
Point, stationary 196
Points, characteristic 96
Points, critical 84
Points, stationary 222 225
Polar subnormal 61
Polar subtangent 61
Potential (of a field) 289
Potential vector field 289
Power series 305
Principal normal 238
Principle of equal effects 369
Principle of superposition of solutions 353
Principle, Runge 383 386
Probability curve 19 484
Probability integral 144
Product of two convergent series 298
Progression, geometric 293 294
Proper rational fraction 121
Proportionate parts, rule of 376
Quadratic interpolation 372
Quadratic trinomial 118 119 123
Quantity, infinitely large 33
Quantity, infinitely small 33
Radius of convergence 305
Radius of curvature 102 243
Radius of second curvature 243
Radius of torsion 243
Rate of change of a function 43
Rate of change, mean 42
Ratio (of a geometric progression) 294
Real numbers 11
Rectangular hyperbola 480
Rectifying plane 238
Reduction formulas 130 135 150
Reduction method 123
Region of convergence 304
Region of integration 246—248
Relative error 367
Remainder 311
Remainder of a series 293 304
Remainder term 311
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