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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
Perpendicular 2 Physics, quantum 230 Piecewise affine function 216 Planar curve 160 Plane, normal 159 Plane, osculating 159 Plane, rectifying 159 Pochhammer symbol 180 Point of function, critical 128 Point of function, singular 128 Point, cluster 8 Point, critical 60 Point, interior 7 Point, saddle 74 Point, stationary 60 Poisson brackets 242 Polar coordinates 88 Polar decomposition 247 Polar part 247 Polar triangle 334 Polarization identity 3 Polygon 274 Polyhedron 274 Polynomial Bernoulli 187 Polynomial function 19 Polynomial, characteristic 39 239 Polynomial, Legendre 177 Polynomial, Taylor 68 Polytope 274 Positive (semi)definite 71 Positively homogeneous function 203 Principal curvature 157 Principal normal 159 Principle, minimax 246 Product of mappings 17 Product, cross 147 Product, Wallis' 184 Projection, Mercator 339 Projection, stereographic 336 Proper Lorentz group 386 Proper Lorentz transformation 386 Proper mapping 26 Property, global 29 Property, local 29 Pseudosphcre 358 Pullback 406 Pullback under diffeomorphism 88 268 Pushforward under diffeomorphism 270 Pythagorean property 3 Quadric, nondegenerate 297 Quantum number, magnetic 272 Quantum physics 230 272 366 Quaternion 382 Radial part 247 Raising operator 371 Rank Lemma 113 Rank of operator 113 Rank theorem 314 Rational function 19 Rational parametrization 390 Rayleigh quotient 72 Real-analytic function 70 Reciprocal function 17 rectangle 30 Rectifying plane 159 Reflection 374 Regression line 228 Regularity of mapping 116 Regularity of mapping 92 Regularity of mapping 124 Regularization 199 Relative topology 10 Remainder 67 Representation, highest weight of 371 Representation, irreducible 371 Representation, spinor 383 Resultant 346 Reverse triangle inequality 4 Revolution, surface of 294 Riemann's zeta function 191 197 Rodrigues' formula 177 Rodrigues' Theorem 382 Rolle's theorem 228 Rotation group 303 Rotation, in 219 300 Rotation, in 303 Rotation, infinitesimal 303 Rule, chain 51 Rule, cosine 331 Rule, Cramer's 41 Rule, del'Hopitars 311 Rule, Leibniz' 240 Rule, sine 331 Rule, spherical, of cosines 334 Rule, spherical, of sines 334 Saddle point 74 Scalar function 12 Scalar multiple of mapping 17 Scalar multiplication 2 Schur complement 304 Second Derivative Test 74 Second-order derivative 63 Second-order partial derivative 61 Section 400 Section, normal 162 Segment of great circle 333 Self-adjoint operator 41 Semicubic parabola 144 Semimajor axis 330 Semiminor axis 330 Sequence, bounded 21 Sequential compactness 25 Series, binomial 181 Series, MacLaurin's 70 Series, Taylor's 70 Set, closed 8 Set, open 7 Shifted factorial 180 Side of spherical triangle 334 Signature, of function at point 73 Signature, of operator 73 Simple zero 101 Sine rule 331 Singular point of diffeomorphism 92 Singular point of function 128 Singularity of mapping 92 Slerp 385 Space, linear 2 Space, metric 5 Space, vector 2 Space-filling curve 211 214 Special linear group 303 Special orthogonal group 302 Special orthogonal group in 219 Special unitary group 377 Spectral theorem 72 245 Sphere 10 Spherical coordinates 261 Spherical function 271 Spherical harmonic function 272 Spherical rule of cosines 334 Spherical rule of sines 334 Spherical triangle 333 Spinor 389 Spinor group 383 Spinor representation 383 389 Spiral 107 138 296 Spiral, logarithmic 350 Standard basis 3 Standard embedding 114 Standard inner product 2 Standard projection 121 Stationary point 60 Steiner's hypocycloid 343 346 Steiner's Roman surface 307 Stereographic projection 306 336 Stirling's asymptotic expansion 197 Stratification 304 Stratum 304 Subcovering 30 Subcovering, finite 30 Subimmersion 315 Submanifold 109 Submanifold at point 109 Submanifold, affine algebraic 128 Submanifold, algebraic 128 Submersion 112 Submersion at point 112 Submersion Theorem 121 Sum of mappings 17 Summation formula of Bernoulli 188 Summation formula of Euler — MacLaurin 194 Supremum 21 surface 110 Surface of revolution 294 Surface, Cayley's 309 Surface, Steiner's Roman 307 Sylvester's law of inertia 73 Sylvester's theorem 376 Symbol, total 241 Symmetric matrix 41 Symmetry identity 201 Tangent bundle 322 403 Tangent mapping 137 225 Tangent space 134 Tangent space, '"intrinsic" description 397 Tangent space, algebraic description 400 Tangent space, geometric 135 Tangent vector 134 Tangent vector field 163 Tangent vector, geometric 322 Taylor polynomial 68 Taylor's formula 68 250 Taylor's series 70 Test, Dirichlet's 189 tetrahedron 274 Theorem, Abel — Ruffini's 102 Theorem, Brouwer's 20 Theorem, Cantor's 211 Theorem, Cauchy's Minimum 206 Theorem, Continuity 77 Theorem, differentiation 78 84 Theorem, Dini's 31 Theorem, Euler's 219 Theorem, Fundamental, of Algebra 291 Theorem, Global Inverse Function 93 Theorem, Hamilton — Cayley's 240 Theorem, Hamilton's 375 Theorem, Heine — Borel's 30 Theorem, Immersion 114 Theorem, implicit function 100 Theorem, Implicit Function, over 106 Theorem, Isomorphism, for groups 380 Theorem, Lagrange's 377 Theorem, Local Inverse Function 92 Theorem, Local Inverse Function, over 105 Theorem, mean value 57 Theorem, Multinomial 241 Theorem, Newton's Binomial 240 Theorem, rank 314 Theorem, Rodrigues' 382 Theorem, Rolle's 228 Theorem, Spectral 72 245 355 Theorem, Submersion 121 Theorem, Sylvester's 376 Theorem, Weierstrass' Approximation 216 Theorema egregium 409 Thermodynamics 290 Tope, standard (n + 1)- 274 topology 10 Topology, algebraic 307 Topology, relative 10 Toroid 349 Torsion 159 Total derivative 43 Total symbol 241 Totally bounded 209 Trace 39 Tractrix 357 Transformation, orthogonal 218 Transition mapping 118 Transpose matrix 39 Transversal 172 Transverse axis 330 Transverse intersection 396 Triangle inequality 4 Triangle inequality, reverse 4 Trisection 326 Tubular neighborhood 319 Umbrella. Whitney's 309 Uniform continuity 28 Uniform convergence 82 Uniformly continuous mapping 28 Unit hyperboloid 390 Unit sphere 124 Unit tangent bundle 323 UNKNOWN 97 Value, critical 60 Vector field 268 404 Vector field, gradient 59 Vector space 2 Vector-valued function 12 Villarceau's circles 327 Wallis' product 184 Wave equation 276 Weierstrass' 185 Weierstrass' approximation theorem 216 Weingartcn mapping 157 Whitney's umbrella 309 wronskian 233 Young's inequality 353 Zeeman effect 272 Zero, simple 101 Zero-set 108 Zeta function, Riemann's 191 Zonal spherical function 271
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