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| Авторизация |
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| Manturov O.V., Matveev N.M. — A course of higher mathematics: linear algebra, analytic geometry, differential calculus of functions of one variable |
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| Предметный указатель |
Abscissa (s) 292
Applying Taylor’s formula in approximate calculations 233—235
Associativity 296
Asymptote(s) 243 420
Asymptote(s) oblique 244 420
Asymptote(s) vertical 244 420
Basic equivalences 180
Basis(es) of a linear space 18
Basis(es), dual adjoint 320
Basis(es), orthogonal in Rn 26
Basis(es), orthogonalization of 307
Basis(es), orthonormal 307
Cauchy — Buniakovski inequality 24
Cauchy’s equivalent 164
Cauchy’s for convergence of a sequence 171
Cauchy’s necessary 164
Cauchy’s necessary, for an extremum to exist 237
Cauchy’s sufficient 164
Characteristic, equation 107 350
Characteristic, polynomial 350
Classification of discontinuity 185
Classification of second-order curves in  132—135 367
Classification of second-order surfaces in  135—140
Cofactor(s) 62
Commutativity 296
Complement 157 374
Complex number(s) 262 425
Complex number(s)  root of 264
Complex number(s) algebraic form of 263 426
Complex number(s) amplitude of 263
Complex number(s) argument of 263
Complex number(s) exponential form of 266 426
Complex number(s) imaginary part of 263
Complex number(s) properties of 425
Complex number(s) real part of 263
Complex number(s) trigonometric form of 263 426
Composition of mappings 160
Computing, derivatives of basic elementary functions 399
Computing, eigenvalues and eigenvectors 104
Computing, rank of a matrix 68
Conditional extrema 448
Cone 372
Coordinate axes 292
Coordinate(s) of a point 11
Coordinate(s) of a vector 12 294
Cylinder of a composite function 199 402
Cylinder of an inverse function 203 403
Cylinder of hyperbolic functions 206
Cylinder of inverse trigonometric functions 199 403
Cylinder, Derivative(s) 192 397
Cylinder, elliptic 139 372
Cylinder, geometrical meaning of 194 398
Cylinder, higher-order 212
Cylinder, hyperbolic 139 372
Cylinder, imaginary elliptic 373
Cylinder, parabolic 140 373
Derivative(s) mechanical meaning of 194 398
Derivative(s) of a vector function 255
Derivative(s) partial 273 434
Derivative(s) properties of 398
Derivative(s) table of, for basic elementary functions 196—197
Determinant(s) basic properties of 54
Determinant(s) Difference of two sets 374
Determinant(s) minor 61
Determinant(s) nth-order 55 326
Determinant(s) properties of 55 326
Determinant(s) second- and third-order 52
Differentials) of a product 211
Differentials) of a quotient 211
Differentials) of a sum 211
Differentials), first 214
Differentials), geometrical meaning of 209 277
Differentials), higher-order 214
Differentials), invariant form of 209
Differentials), nth 214
Directed line segment 292
Direction cosines 27
Discontinuity(ies) 393
Discontinuity(ies) of the first kind 186
Discontinuity(ies) of the second kind 186
Discontinuity(ies), classification of 185 393
Discontinuity(ies), removable 188
Distance, between skew lines in R 3 313
Distance, between two points 24
Domain(s) 432
Eccentricity 369
Eigenvalue(s) 104 349
Eigenvector(s) 103 349
Eigenvector(s) of a matrix 105
ellipse 369
Ellipse, imaginary 133 370
Ellipsoid 136 371
Elliptic, cylinder 139
Elliptic, paraboloid 138
Equation(s) in coordinate form 31
Equation(s) in vector form 31
Equation(s) of a plane 31 310
Equation(s) vector 311
Equation(s), coordinate 311
Equation(s), matrix-vector 91
Equation(s), parametric, of a curve 258
Equation(s), parametric, of a straight line 311
Equivalence, class 294
Equivalence, relation 293
Evaluation of indeterminate forms 218—225
Evaluation of limits by Taylor’s formula 231
Examples of algorithms 376
Existence of intermediate values 395
Expanding a determinant by a row (column) 330—333
Finding the canonical form of a second-order curve or surface 140—142
Formula (s) with remainder in Lagrange’s form 227 410
Formula (s) with remainder in Peano’s form 227 410
Formula (s), Cramer’s 57 78 88 345
Formula (s), De Moivre’s 264
Formula (s), Euler’s 266
Formula (s), Leibniz 212 406
Formula (s), Maclaurin’s 227
Formula (s), Taylor’s 226 282 441
Fredholm’s alternatives 100 347
Function(s) 158—159 375
Function(s) of a real variable with real values 159—160
Function(s) of several variables 270
Function(s), argument of 159
Function(s), basic elementary 174
Function(s), composite 160
Function(s), composition of 160
Function(s), continuous at a point 173
Function(s), decreasing 161 236 414
Function(s), differentiable 207 274 4 04
Function(s), differential of 207
Function(s), domain of 159
Function(s), exponential 174 384
Function(s), hyperbolic 204 404
Function(s), implicit 285 443
Function(s), increasing 161 236 414
Function(s), infinitely large 178 388
Function(s), infinitesimal 178 388
Function(s), inverse of 160
Function(s), inverse trigonometric 175
Function(s), Lagrange’s 290
Function(s), limit of 377
Function(s), linearized 209
Function(s), logarithmic 174 384
Function(s), monotone 161
Function(s), power 174 384
Function(s), range of 159
Function(s), rational 174 384
Function(s), represented parametrically 258 424
Function(s), smooth 212
Function(s), superposition of 160
| Function(s), trigonometric 175
Function(s), value of 159
Fundamental theorem of algebra 269 430
Gaussian elimination 79 339
General procedure for investigating, functions 246 421
Half-line, negative 292
Half-line, positive 292
Hodograph of a vector function 258
Hyperbola 133 369
Hyperbolic, cosine 204
Hyperbolic, cylinder 139
Hyperbolic, derivative of 206
Hyperbolic, functions 204
Hyperbolic, graphs of 204—205
Hyperbolic, paraboloid 138
Hyperbolic, properties of 204—205
Hyperbolic, sine 204
Hyperbolic, tangent 204
Hyperboloid of one sheet 136 371
Hyperboloid of two sheets 137 371
Identity condition for two polynomials 269
Imaginary, cone 372
Imaginary, ellipse 133
Increment in a function 273
Increment partial 273
Infinitesimal(s) comparison of 179
Infinitesimal(s) equivalent 179
Infinitesimal(s) principal part of 181
intersection of two sets 374
Invariant form of differential 208 276
Isomorphism 305
Isotherm 272
Jordan box 359
Jordan form of a matrix 120 359
Kronecker — Capelli theorem 78 83 105 343
Lagrange multipliers 290
Leibniz notation for the derivative of a function 211
Level surface 272
Limit (s) 165
Limit (s) first remarkable 171
Limit (s) left-hand 184 377
Limit (s) of a function 168
Limit (s) of a ratio of polynomials 166—167
Limit (s) of a sequence 165
Limit (s) one-sided 184 377 393
Limit (s) right-hand 184 377
Limit (s) second remarkable 170
Linear 298
Linear operators 35 314
Linear operators, canonical form of 120
Linear operators, characteristic polynomial of 109 350
Linear operators, degenerate 98
Linear operators, eigenvector of 103
Linear operators, kernel of 97
Linear operators, matrix of 38 314
Linear operators, nondegenerate 98
Linear operators, product of, by a number 39 315
Linear operators, range of 97
Linear operators, sum of 39 315
Linearization 209 405
Local extrema 236
Mapping(s) bijective 160
Mapping(s) composition of 160
Mapping(s) injective 160
Mapping(s) surjective 160
Matrix(es) 38
Matrix(es) characteristic polynomial of 107
Matrix(es) determinant of 57
Matrix(es) diagonal 51
Matrix(es) eigenvalue of 107 350
Matrix(es) eigenvector of 350
Matrix(es) elementary transformation of 79
Matrix(es) inverse of 90 316
Matrix(es) of a linear operator in a new basis 117
Matrix(es) orthogonal 49 319
Matrix(es) rank of 64 333
Matrix(es) root of 350
Matrix(es) similar 109 354—355
Matrix(es) spectrum of 109
Matrix(es) stepped form of 68
Matrix(es) symmetric 48 319
Matrix(es) transpose of 48
Matrix(es) transposed 47
Matrix(es) triangular form of 59
Mechanical meaning of a vector function of a scalar argument 355 356
Minor(s) 61
n-Dimensional coordinate, Euclidean space 28
n-Dimensional coordinate, linear space 15
Notion of algorithmic and nonalgorithmic proofs 375
One-sided continuity 393
Operator(s) adjoint 46 319 321
Operator(s) canonical form of 121 358
Operator(s) eigenvalue of 349
Operator(s) eigenvector of 349
Operator(s) elementary 68
Operator(s) kernel of 346
Operator(s) linear 35
Operator(s) range of 346
Operator(s) self-adjoint 47 319
Ordered vector triple 72
Ordered vector triple, left-handed 72
Ordered vector triple, right-handed 72
Ordinate(s) 292
Pair of imaginary intersecting planes 373
Pair of imaginary intersecting straight lines 370
Pair of imaginary parallel lines 370
Pair of imaginary planes 373
Pair of intersecting planes 373
Pair of intersecting straight lines 370
Pair of merged parallel lines 371
Pair of merged parallel planes 373
Pair of parallel lines 370
Pair of parallel planes 373
parabola 134 370
Parabolic cylinder 140
Paraboloid, elliptic 138 372
Paraboloid, hyperbolic 138 372
Pascal’s triangle 213
Permutation(s) 56 323
Permutation(s) even 56
Permutation(s) identity 56
Permutation(s) odd 56
Permutation(s) properties of 323
Phospital’s 218 221 409
Point(s) initial 292
Point(s) of inflection 243
Point(s) stationary 237
Point(s) terminal 272
Point(s), critical 237
Product of a matrix by a number 39
Product of a vector and a real number 13
Product of sets 156
Product of two matrices 39
Product scalar, of two vectors 22 305
Product, vector 71
Properties of derivatives of vector functions 423
Properties of functions continuous at a point 183
Properties of functions having limits 172—173 377
Properties of infinitesimal functions 177
Properties of variables 195
Properties, interval 189
Proposition(s) 374
Proposition(s), conjunction of 374
Proposition(s), disjunction of 374
Proposition(s), false 354
Proposition(s), true 374
Quadratic form 123 360
Quadratic form, matrix of 123 360
Quadratic form, rank of 129
Quadratic form, signature of 129
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