Авторизация
Поиск по указателям
Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis I(Cambridge Studies in Advanced Mathematics #86), Vol. 1
Обсудите книгу на научном форуме Нашли опечатку?
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 |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
51 185 (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) 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) 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, 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, 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
Реклама
mapping 
function, Wcierstrass' 
, on subset 
|
|
О проекте