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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
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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Название: A course of higher mathematics: linear algebra, analytic geometry, differential calculus of functions of one variable

Авторы: Manturov O.V., Matveev N.M.

Аннотация:

Книга "Курс высшей математики" представлена на английском языке.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 470

Добавлена в каталог: 08.12.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $R^{2}$      132—135 367
Classification of second-order surfaces in $R^{3}$      135—140
Cofactor(s)      62
Commutativity      296
Complement      157 374
Complex number(s)      262 425
Complex number(s) $\textit{n}th$ 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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