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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. 1Авторы: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2007Количество страниц: 422Добавлена в каталог: 11.06.2008Операции: Положить на полку |
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Предметный указатель
Gaussian curvature 157 General linear group 38 Generalized binomial coefficient 181 Generator, infinitesimal 163 Geodesic 361 Geometric tangent space 135 Geometric-arithmetic inequality 351 Global inverse function theorem 93 Gradient 59 Gradient operator 59 Gradient vector field 59 Gram — Schmidt orthonormalization 356 Gram's matrix 39 Graph 107 203 Grassmann's identity 331 Great circle 333 Greatest lower bound 21 Group action 162 163 238 Group, covering 383 386 389 Group, general linear 38 Group, Lorentz 386 Group, orthogonal 73 124 219 Group, permutation 66 Group, proper Lorentz 386 Group, special linear 303 Group, special orthogonal 302 Group, special orthogonal, in 219 Group, special unitary 377 Group, spinor 383 Hadamard's inequality 152 356 Hadamard's lemma 45 Hamilton — Cayley, Theorem of 240 Hamilton's Theorem 375 Harmonic function 265 Heine — Borel theorem 30 Helicoid 296 Helix 107 138 296 Hermitian matrix 385 Heron's formula 330 hessian 71 Hessian matrix 71 Highest weight of representation 371 Hilbert — Schmidt norm 39 Hilbert's Nullstellensatz 311 Hoelder continuity 213 Hoelder's inequality 353 Holomorphic 105 Holonomy 363 Homeomorphic 19 Homeomorphism 19 Homogeneous function 203 Homomorphism of Lie algebras 170 Homomorphism of rings, induced 401 Hopf fibration 307 383 Hopf mapping 306 Hyperbolic reflection 391 Hyperbolic screw 390 Hyperboloid of one sheet 298 Hyperboloid of two sheets 297 Hypersurface 110 145 Hypocycloid 342 Hypocycloid, Steiner's 343 346 Identity mapping 44 Identity, Euler's 228 Identity, four-square 377 Identity, Grassmann's 331 364 Identity, Jacobi's 332 Identity, Lagrange's 332 Identity, parallelogram 201 Identity, polarization 3 Identity, symmetry 201 Image, inverse 12 Immersion 111 Immersion at point 111 Immersion Theorem 114 Implicit definition of function 97 Implicit differentiation 103 Implicit function theorem 10 Implicit Function Theorem over C 106 Incircle of Steiner's hypocycloid 344 indefinite 71 Index, of function at point 73 Index, of operator 73 Induced action 163 Induced homomorphism of rings 401 Inequality, Cauchy — Schwarz' 4 Inequality, Cauchy — Schwarz', generalized 245 Inequality, geometric-arithmetic 351 Inequality, Hadamard's 152 Inequality, isopcrimetric for triangle 352 Inequality, Kantorovich's 352 Inequality, Minkowski's 353 Inequality, reverse triangle 4 Inequality, triangle 4 Inequality, Young's 353 Inequality,Inequality, Hoelder's 353 Infimum 21 Infinitesimal generator 56 163 239 303 365 366 Initial condition 55 163 Inner derivation 169 Integral formula for remainder in Taylor's formula 67 68 Integral, Frullani's 81 Integrals, Laplace's 254 Interior 7 Interior point 7 Intermediate value property 33 interval 33 Intrinsic property 408 Invariance of dimension 20 Invariance of Laplacian under orthogonal transformations 230 Inverse image 12 Inverse mapping 55 Irreducible representation 371 Isolated zero 45 Isomorphism Theorem for groups 380 Isoperimetric inequality for triangle 352 Iteration method, Newton's 235 Iwasawa decomposition 356 Jacobi matrix 48 Jacobi's identity 169 332 Jacobi's notation for partial derivative 48 k-linear mapping 63 Kantorovich's inequality 352 Lagrange function 149 Lagrange multipliers 150 Lagrange's identity 332 Lagrange's theorem 377 Laplace operator 229 265 270 Laplace's integrals 254 Laplacian 229 Laplacian in cylindrical coordinates 263 Laplacian in spherical coordinates 264 Latus rectum 330 Laws, DeMorgan's 9 Least upper bound 21 Lebesgue number of covering 210 Legendre function, associated 177 Legendre polynomial 177 Legendre's equation 177 Leibniz — Hormander's formula 243 Leibniz' rule 240 Lemma, Hadamard's 45 Lemma, Morse's 131 Lemma, Rank 113 Lemniscate 323 Lemniscatic sine 180 287 Lemniscatic sine, addition formula for 288 313 Length of vector 3 Level set 15 Lie algebra 169 231 332 Lie bracket 169 Lie derivative 404 Lie derivative at point 402 Lie group, linear 166 Lie's product formula 171 Light cone 386 Limit of mapping 12 Limit of sequence 6 Linear Lie group 166 Linear mapping 38 Linear operator, adjoint 39 Linear partial differential operator 241 Linear regression 228 Linear space 2 Linearized problem 98 Lipschitz constant 13 Lipschitz continuous 13 Local Inverse Function Theorem 92 Local Inverse Function Theorem over 105 Locally isometric 341 Lorentz group 386 Lorentz group, proper 386 Lorentz transformation 386 Lorentz transformation, proper 386 Lowering operator 371 Loxodrome 338 Maclaurin's series 70 Manifold 108 109 Manifold at point 109 Mapping 12 Mapping, 51 Mapping, adjoint 380 Mapping, closed 20 Mapping, continuous 13 Mapping, derived 43 Mapping, differentiable 43 Mapping, identity 44 Mapping, inverse 55 Mapping, k times continuously differentiable 65 Mapping, k-linear 63 Mapping, linear 38 Mapping, of manifolds 128 Mapping, open 20 Mapping, partial 12 Mapping, proper 26 206 Mapping, tangent 225 Mapping, uniformly continuous 28 Mapping, Weingarten 157 Mass 290 Matrix 38 Matrix, antisymmetric 41 Matrix, cofactor 233 Matrix, hermitian 385 Matrix, Hessian 71 Matrix, Jacobi 48 Matrix, orthogonal 219 Matrix, symmetric 41 Matrix, transpose 39 Mean value theorem 57 Mercator projection 339 Method of least squares 248 Metric space 5 Minimal principle 246 Minkowski's inequality 353 Minor of matrix 41 Modification 244 Monomial function 19 Morse function 244 Morse's lemma 131 Moving frame 267 Multi-index 69 Multinomial theorem 241 Multipliers, Lagrange 150 nabla 59 Negative (semi)definite 71 Neighborhood 8 Neighborhood in subset 10 Neighborhood, open 8 Nephroid 343 Newton's Binomial Theorem 240 Newton's equation 290 Newton's iteration method 235 Nicomedes' conchoid 325 Nomographic transformation 384 Nondegenerate critical point 75 Norm 27 Norm, Euclidean 3 Norm, Euclidean, of linear mapping 39 Norm, Frobenius 39 Norm, Hilbert — Schmidt 39 Norm, operator 40 normal 146 Normal curvature 162 Normal plane 159 Normal section 162 Normal space 139 Nullity, of function at point 73 Nullity, of operator 73 Nullstellensatz, Hubert's 311 One-parameter family of lines 299 One-parameter group of diffeomorphisms 162 One-parameter group of invertible linear mappings 56 One-parameter group of rotations 303 Open ball 6 Open ball in subset 10 Open covering 30 Open mapping 20 Open neighborhood 8 Open neighborhood in subset 10 Open set 7 Operator norm 40 Operator, anti-adjoint 41 Operator, self-adjoint 41 Orbit 163 orbital angular momentum quantum number 272 Ordinary cusp 144 Ordinary differential equation 55 177 269 Orthocomplemcnt 201 Orthogonal group 73 Orthogonal matrix 219 Orthogonal projection 201 Orthogonal transformation 218 Orthogonal vectors 2 Orthonormal basis 3 Orthonormalization, Gram — Schmidt 356 Osculating circle 361 Osculating plane 159 Paraboloid, elliptic 297 Parallel translation 363 Parallelogram identity 201 PARAMETER 97 Parameter, Cayley — Klein 376 380 391 Parametrization 111 Parametrization, of orthogonal matrix 364 375 Parametrized set 108 Partial derivative 47 Partial derivative, second-order 61 Partial differential operator 164 Partial differential operator, linear 241 Partial mapping 12 Partial summation formula of Abel 189 Partial-fraction decomposition 183 Partially differentiable 47 Particle without spin 272 Pendulum, Foucault's 362 Periapse 330 Period 185 Period lattice 184 185 Periodic 190 Permutation group 66
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