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| Авторизация |
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| Demidovich B. (ed.) — Problems in mathematical analysis |
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| Предметный указатель |
Absolute error 367
Absolute value of a real number 11
Absolutely convergent series 296 297
Acceleration vector 236
Adams' formula 390
Adams' method 389 390 392
Agnesi, witch of 18 156 480
Algebraic functions 48
Angle between two surfaces 219
Angle of contingence 102 243
Angle of contingence of second kind 243
Antiderivative 140 141
Antiderivative, generalized 143
Approximate numbers 367
Approximate numbers, addition of 368
Approximate numbers, division of 368
Approximate numbers, multiplication of 368
Approximate numbers, powers of 368
Approximate numbers, roots of 368
Approximate numbers, subtraction of 368
Approximation, successive 377 385
Arc length of a curve 158—161
Arc length of a space curve 234
Archimedes, spiral of 20 65 66 105 487
Area in polar coordinates 155 256
Area in rectangular coordinates 153 256
Area of a plane region 256
Area of a surface 166—168 259
Argument 11
Astroid 20 63 105 486
Asymptote 93
Asymptote, left horizontal 94
Asymptote, left inclined 94
Asymptote, right horizontal 93
Asymptote, right inclined 93
Asymptote, vertical 93
Bending point 84
Bernoulli's equation 333
Bernoulli's lemniscate 155 486
Beta-function 146 150
Binormal 238
boundary conditions 363
Branch of a hyperbola 20 480
Broken-line method, Euler's 326
Cardioid 20 105 486
Catenary 104 105 484
Catenoid 168
Cauchy's integral test 295
Cauchy's test 293 295
Cauchy's theorem 75 326
Cavalieri's "lemon" 165
Centre of curvature 103
Change of variable 211—217
Change of variable in a definite integral 146
Change of variable in a double integral 252—254
Change of variable in an indefinite integral 113
Characteristic equation 356
Characteristic points 96
Chebyshev's conditions 127
Chord method 376
circle 20 104
Circle of convergence 306
Circle of curvature 103
Circle, osculating 103
Circulation of a vector 289
Cissoid 232
Cissoid of Diodes 18 485
Clairaut's equation 339
Closed interval 11
Coefficients, Fourier 318 393 394
Comparison Test 143 293 294
Composite function 12 49
Concave down 91
Concave up 91
Concavity, direction of 91
Conchoid 232
Condition, Lipschitz 385
Conditional extremum 223—225
Conditionally (not absolutely) convergent series 296
Conditions, boundary 363
Conditions, Chebyshev's 127
Conditions, Dirichlet 318 319
Conditions, initial 323 363
Contingence, Angle of 102 243
Continuity of functions 36
Continuous function 36
Continuous function, properties of 38
Convergence, circle of 306
Convergence, interval of 305
Convergence, radius of 305
Convergence, region of 304
Convergence, uniform 306
Convergent improper integral 143 270
Convergent Series 293
Coordinates of centre of gravity 170
Coordinates, generalized polar 255
Correct decimal places in a broad sense 367
Correct decimal places in a narrow sense 367
Cosine curve 481
Cotangent curve 481
Coupling equation 223
Critical point of the second kind 92
Critical points 84
Cubic parabola 17 105 234 480
Curl of a vector field 288
Curvature, centre of 103
Curvature, circle of 103
Curvature, of a curve 102 242
Curvature, radius of 102
Curvature, second 243
Curve, cosine 481
Curve, cotangent 481
Curve, discriminant 232 234
Curve, Gaussian 92
Curve, integral 322
Curve, logarithmic 484
Curve, probability 19 484
Curve, sine 481
Curve, tangent 481
Cusp 230
Cycloid 105 106 486
d'Alembert's test 295
Decreasing function 83
Definite integral 138
DEL 288
Dependent variable 11
Derivative 43
Derivative of a function in a given direction 193
Derivative of an implicit function 57
Derivative of an inverse function 57
Derivative of functions, represented parametrically 57
Derivative of the second order 66
Derivative, left-hand 44
Derivative, logarithmic 55
Derivative, nth 67
Derivative, right-hand 44
Derivative, second 66
Derivatives of higher orders 66—69
Derivatives, one-sided 43
Derivatives, table of 47
Descartes, folium of 20 21 232 485
Determinant, functional 264
Determining coefficients, first method of 122
Determining coefficients, second method of 122
Diagonal table 389
Dicriminant curve 232 234
Difference of two convergent series 298
Differential equation 322
Differential equation, homogeneous linear 349
Differential equation, inhomogeneous linear 349
| Differential equations of higher powers, first-order 337
Differential equations, first-order 324
Differential equations, forming 329
Differential equations, higher-order 345
Differential equations, linear 349 351
Differential of an arc 101 234
Differential, first-order 71
Differential, higher-order 198
Differential, principal properties of 72
Differential, second 198
Differential, second-order 72
Differential, total, integration of 202—204
Differentials of third and higher orders 72
Differentials, method of 343
Differentiating a composite function 47
Differentiation 43
Differentiation of implicit functions 205—208
Differentiation, tabular 46
Diodes, cissoid of 18 485
Direction field 325
Direction of concavity 91
Dirichlet, conditions 318 319
Dirichlet, function 40
Dirichlet, series 295 296
Dirichlet, Theorem 318
Discontinuity 37
Discontinuity of the first kind 37
Discontinuity of the second kind 38
Discontinuity, infinite 38
Discontinuity, removable 37
Discontinuous function 270
Discriminant 222
Divergence of a vector field 288
Divergent improper integral 143 270
Divergent series 293 294
Domain 11
Domain of definition 11
Double integral 246
Double integral in curvilinear coordinates 253
Double integral in polar coordinates 252
Double integral in rectangular coordinates 246
Double point 230
Elimination, method of 359
ellipse 18 20 104 485
Energy, kinetic 174
Envelope of a family of plane curves 232
Envelope, equations of 232
Epicycloid 283
Equal effects, principle of 369
Equation of a normal 60 218
Equation of a tangent 60
Equation of a tangent plane 218
Equation with variables separable 327 328
Equation, Bernoulli's 333
Equation, characteristic 356
Equation, Clairaut's 339
Equation, coupling 223
Equation, differential 322
Equation, Euler's 357
Equation, exact differential 335
Equation, first-order differential 324
Equation, homogeneous 330 351 356
Equation, homogeneous linear differential 332 349
Equation, inhomogeneous 349 351 356
Equation, Lagrange's 339
Equation, Laplace's 289 291
Equation, linear 332
Equivalent functions 33
Error, absolute 367
Error, limiting absolute 367
Error, limiting relative 367
Error, relative 367
Euler integral 146
Euler — Poisson integral 272
Euler's broken-line method 326
Euler's equation 357
Even function 13
Evolute of a curve 103
Evolvent of a circle 486
Evolvent of a curve 104
Exact differential equation 335
Exponential functions 49 55 483
Extremal point 84
Extremum of a function 83 83 222
Extremum, conditional 223—225
Factor, integrating 335
Field theory 288—292
Field, direction field 325
Field, nonstationary scalar or vector 288
Field, potential vector 289
Field, scalar 288
Field, solenoidal vector 289
Field, stationary scalar or vector 288
Field, vector 288
First-order differential 71
First-order differential equations 324
Flow lines 288
Flux of a vector field 288
Folium of Descartes 20 21 232 485
Force lines 288
Form, Lagrange's 311
Formula, Adams' 390
Formula, Green's 276 281 282
Formula, Lagrange's 145
Formula, Lagrange's interpolation 374
Formula, Leibniz 67
Formula, Maclaurin's 77 220
Formula, Newton — Leibniz 140 141 275
Formula, Newton's interpolation 372
Formula, Ostrogradsky — Gauss 286—288
Formula, parabolic 382
Formula, Simpson's 382—384
Formula, Stokes' 285 286 289
Formula, Taylor's 77 220
Formula, trapezoidal 382
Formulas, reduction 130 135
Four-leafed rose 487
Fourier coefficients 318 393 394
Fourier series 318 319
Fraction, proper rational 121
Function 11
Function of a function 12
Function, composite 12 49
Function, continuous 36
Function, continuous, properties of 38
Function, decreasing 83
Function, Dirichlet 40
Function, discontinuous 270
Function, even 13
Function, implicit 12
Function, increasing 83
Function, Lagrange 223 224
Function, multiple-valued 11
Function, periodic 14
Function, single-valued 11
Function, vector 235
Functional determinant 264
Functional series 304
Functions, algebraic 48
Functions, equivalent 33
Functions, exponential 49 55 483
Functions, hyperbolic 49 484
Functions, hyperbolic, integration of 133
Functions, inverse 12
Functions, inverse circular 48
Functions, inverse hyperbolic 49
Functions, inverse trigonometric 482 483
Functions, linearly dependent 349
Functions, linearly independent 349
Functions, logarithmic 49
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