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Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis I(Cambridge Studies in Advanced Mathematics #86), Vol. 1
Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis I(Cambridge Studies in Advanced Mathematics #86), Vol. 1

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Название: Multidimensional Real Analysis I(Cambridge Studies in Advanced Mathematics #86), Vol. 1

Авторы: Duistermaat J.J., Kolk J.A.C.

Аннотация:

The authors, affiliated with Utrecht University, present a two-volume work on the theory of vector-valued functions in multidimensional Euclidean space. This volume is devoted to differentiation, with material on differentiable functions on Rn and differentiable manifolds embedded in Rn. Chapters cover continuity, differentiation, inverse function and implicit function theorems, manifolds, and tangent spaces. Chapter exercises illustrate a variety of applications in mathematics and physics. The book can be used as a text for a course for students who wish to go on to more advanced study, as a source of problems for a seminar, or for self study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 422

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1$ mapping      51
$\wp$ function, Wcierstrass'      185
(Geometric) tangent vector      322
Abel — Ruffini theorem      102
Abel's partial summation formula      189
Abelian group      169
Acceleration      159
action      238 366
Action, group      162
Action, induced      163
Addition      2
Addition, formula for lemniscatic sine      288
Adjoint linear operator      39 398
Adjoint mapping      168 380
Affine function      216
Airy' function      256
Airy's differential equation      256
Algebraic topology      307
Analog formula      395
Analogs of Delambre — Gauss      396
angle      148 219 301
Angle of spherical triangle      334
Angle-preserving      336
Angular momentum operator      230 264 272
Anti-adjoint operator      41
Anticommutative      169
Antisymmetric matrix      41
Approximation, best affine      44
Argument function      88
Associated Legendre function      177
Associativity      2
Astroid      324
Asymptotic expansion      197
Asymptotic expansion, Stirling's      197
Automorphism      28
Autonomous vector field      163
Axis of rotation      219 301
Ball, closed      8
Ball, open      6
Basis, orthonormal      3
Basis, standard      3
Bernoulli function      190
Bernoulli number      186
Bernoulli polynomial      187
Bernoulli's summation formula      188 194
Best affine approximation      44
Bifurcation set      289
binomial      159
Binomial coefficient, generalized      181
Binomial series      181
Biregular      160
Bitangent      327
Boost      390
Boundary      9
Boundary in subset      11
Bounded sequence      21
Brouwer's theorem      20
Bundle, tangent      322
Bundle, unit tangent      323
Cagnoli's formula      395
Canonical      58
Cantor's theorem      211
Cardioid      286 299
Cartan decomposition      247 385
Casimir operator      231 265 370
Catenary      295
Catenoid      295
Cauchy sequence      22
Cauchy — Schwarz inequality      4
Cauchy — Schwarz inequality, generalized      245
Cauchy's Minimum Theorem      206
Caustic      351
Cayley's surface      309
Cayley-Klein parameter      376 380 391
Chain rule      51
Change of coordinates, (regular) $C^k$      88
Characteristic function      34
Characteristic polynomial      39 239
Chart      111
Christoffel symbol      408
Circle, osculating      361
Circles. Villarceau's      327
Cissoid, Diodes'      325
Clifford algebra      383
Clifford multiplication      379
Closed ball      8
Closed ball in subset      10
Closed mapping      20
Closed set      8
Closure      8
Closure in subset      11
Cluster point      8
Cluster point in subset      10
Cndomorphism      38
Codimension of submanifold      112
Coefficient of matrix      38
Coefficient, Fourier      190
Cofactor matrix      233
Commutativity      2
Commutator      169 217 231 407
Commutator relation      231 367
Compactness      25 30
Compactness, sequential      25
Complement      8
Complementary matrix      41
Completeness      22 204
Complex-differentiable      105
Component function      2
Component of vector      2
Composition of mappings      17
Computer graphics      385
Conchoid, Nicomedes'      325
conformal      336
Conjugate axis      330
Connected component      35
Connectedness      33
Connection      408
Conservation of energy      290
Continuity      13
Continuity theorem      77
Continuity. Holder      213
Continuous mapping      13
Continuously differentiable      51
Contraction      23
Contraction factor      23
Contraction Lemma      23
Convergence      6
Convergence, uniform      82
Convex      57
Coordinate function      19
Coordinate of vector      2
Coordinates, change of, (regular) $C^k$      88
Coordinates, confocal      267
Coordinates, cylindrical      260
Coordinates, polar      88
Coordinates, spherical      261
Coordinatization      111
Cosine rule      331
Cotangent bundle      399
Cotangent space      399
Covariant derivative      407
Covariant differentiation      407
Covering group      383 386
Covering group, open      30
Cramer's rule      41
Critical point      60
Critical point of diffeomorphism      92
Critical point of function      128
Critical point, nondegenerate      75
Critical value      60
Cross product      147
Cross product operator      363
Curvature form      363 410
Curvature of curve      159
Curvature, Gaussian      157
Curvature, normal      162
Curvature, principal      157
Curve      110
Curve, differentiable (space)      134
Curve, space-filling      211
Cusp, ordinary      144
Cycloid      141 293
Cylindrical coordinates      260
d'Alembert's formula      277
Decomposition, Cartan      247
Decomposition, Iwasawa      356
Decomposition, polar      247
DEL      59
Delambre — Gauss, analogs of      396
DeMorgan's laws      9
Dense in subset      203
Derivation      404
Derivation at point      402
Derivation, inner      169
Derivative      43
Derivative, directional      47
Derivative, partial      47
Derived mapping      43
Descartes' folium      142
Diameter      355
Diffeomorphism, $C^k$      88
Diffeomorphism, orthogonal      271
Differentiability      43
Differentiable mapping      43
Differentiable, continuously      51
Differentiable, partially      47
Differential      400
Differential at point      399
Differential equation, Airy's      256
Differential equation, for rotation      165
Differential equation, Legendre's      177
Differential equation, Newton's      290
Differential equation, ordinary      55 163 177 269
Differential form      400
Differential operator, linear partial      241
Differential operator, partial      164
Differentiation theorem      78 84
Dimension of submanifold      109
Dini's theorem      31
Diodes' cissoid      325
Directional derivative      47
Dirichlet's test      189
Disconnectedness      33
Discrete      396
Discriminant      347
Discriminant locus      289
Distance. Euclidean      5
Distributivity      2
Divergence in arbitrary coordinates      268
Divergence, of vector field      166
Dual basis for spherical triangle      334
Dual vector space      398
Duality, definition by      404 406
Duplication formula for (lemniscatic) sine      180
e l'Hopital's rule      311
Eccentricity      330
Eccentricity vector      330
Egregium, Theorema      409
Eigenvalue      72 224
Eigenvector      72 224
Elimination      125
Elimination theory      344
Elliptic curve      185
Elliptic paraboloid      297
Embedding      111
Energy, kinetic      290
Energy, potential      290
Energy, total      290
Entry of matrix      38
Envelope      348
Epicycloid      342
Equality of mixed partial derivatives      62
equation      97
Equivariant      384
Euclidean distance      5
Euclidean norm      3
Euclidean norm of linear mapping      39
Euclidean space      2
Euler operator      231 265
Euler — Maclaurin summation formula      194
Euler's formula      300
Euler's identity      228
Euler's theorem      219
Evolute      350
Excess of spherical triangle      335
Exponential      55
Fiber bundle      124
Fiber bundle of mapping      124
Finite intersection property      32
Finite part of integral      199
Fixed point      23
Flow of vector field      163
Focus      329
Folium, Descartes'      142
Formula, analog      395
Formula, Cagnoli's      395
Formula, D'Alembert's      277
Formula, Euler's      300
Formula, Heron's      330
Formula, Leibniz — Hormander's      243
Formula, Rodrigues'      177
Formula, Taylor's      68
Formulae, Frenet — Serret's      160
Forward (light) cone      386
Foucault's pendulum      362
Four-square identity      377
Fourier analysis      191
Fourier coefficient      190
Fourier series      190
Fractional linear transformation      384
Frenet — Serret's formulae      160
Frobenius norm      39
Frullani's integral      81
Function of several real variables      12
Function, $C^{\infty}$, on subset      399
Function, affine      216
Function, Airy      256
Function, Bernoulli      190
Function, characteristic      34
Function, complex-differentiable      105
Function, coordinate      19
Function, holomorphic      105
Function, Lagrange      149
Function, monomial      19
Function, Morse      244
Function, piecewise affine      216
Function, polynomial      19
Function, positively homogeneous      203 228
Function, rational      19
Function, real-analytic      70
Function, reciprocal      17
Function, scalar      12
Function, spherical      271
Function, spherical harmonic      272
Function, vector-valued      12
Function, zonal spherical      271
Functional dependence      312
Functional equation      175 313
Fundamental theorem of algebra      291
Gauss mapping      156
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