|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Loomis L.H., Sternberg S. — Advanced calculus |
|
|
|
| Предметный указатель |
Absolute convergence, of an infinite series 221
Absolute value 121 242
Absolutely integrable function 351
Adjoint of T 85
Affine independence 81
Affine span 56
Affine subspace 40 52
Affine transformation 53
Algebra 30 46
Algebra of matrices 92
Algebra, Banach 223
Alternating tensor 310
Amplitude 292
Analytic plane  10
Annihilator 84
Antisymmetric tensor 310
Associative law, for composition 14
Atlas 364
Ball, closed 124
Ball, open 123 196
Banach algebra 223
Banach space 217
Banach — Tarski paradox 321
Basis 71
Basis for pre-Hilbert space 254
Basis in Hom(V,W) 96
Basis isomorphism 72
Basis, dual 82
Basis, infinite 75
Bessel's inequality 254
Bijective 12
Bilinear 67
Bilinear functionals 305ff
Block decompositions 65ff
Bound variable 2
Boundary 198
Boundary-value problem 294ff
Bounded below 128
Bounded function 122
Bounded linear mapping 127
Bounded set 123
Braces 7
Calculus of variations 182ff
Canonical basis 104
Canonical transformation 558 560
Cartesian axes 38
Cartesian product of two sets 9
Cartesian product, of an indexed collection 14
Cauchy sequence 216
Cellulation 473
Center of mass 529
Center, of gravity 349
Central force 523 564
Centrifugal force 517
Centrifugal potential 517
Chain rule 153
Change of basis 94
Change of variable formula 342 355
Characteristic function of a set 12
Characteristic function, Fourier transform 337
Characteristic polynomial 259
Classical mechanics 509
Closed set 124 197
Closure 198
Codimension 80
Codomain 12
Cofactor 315
Column space (of a matrix) 91
Column vector 93
Commutative diagram 86
Compact transformation 264
Compactness on a manifold 403
Compactness, in general topology 214
Compactness, sequential 206
Compatible atlases 370
Complement 17
Complementary subspaces 57
Completeness 217
Completion 222
Complex conjugation 241
Complex normed linear space 244
complex numbers 240ff
Complex vector space 24 241
Complexification 244
Component 58
Composite truth-functional forms 5
Composite-function rule 143
composition 14
Configuration space 509
Conjugate space 82
Connectives, logical 3
Conservation of energy 521
Conservation, laws 521
Conservation, of angular momentum 523
Constant coefficient equation 278
Constrained maximum 173f
Content 332
Contented function 339
Contented sets 331f
Continuity 126 196 201 203
Contraction mapping 229
Contravariant vector 95
Convergence of infinite series 221
Convergence, sequential 202
Convex set 125
Coordinate 43 72
Coordinate correspondence 36f
Coordinate functional 33 72
Coordinate isomorphism 72
Coordinate n-tuple 72
Coordinate projection 43
Correspondence 9
Coset 52
Cotangent bundle 511
Covariant tensor 307
Covariant vector 95
Cramer's rule 101 315
Critical point 161 188ff
Cylindrical coordinates 345 (Ex. 11.5)
De Morgan's law 17
Definite (form) 115
Degree (of a polynomial) 64
Dense subset 212
density 408
Dependent set of vectors 73
Derivative 146
Derivative in a Banach algebra 226
Derivative over  242
Derivative, directional 147
Determinant 99ff 108 312ff
Diagonal matrix 262
Diffeomorphism 376
Differentiable manifolds 363 369ff
Differential 142
Differential forms 390f
Differential geometry 459
Differentiation under the integral sign 181
DIMENSION 78
Dimensional identities 78f 84
Direct sum 56
Directed frame 9
Directed line segment 37
Directional derivative 147
Disjoint (family of sets) 18
Distance between vectors 122
Distance, in a metric space 196
Divergence theorem 421
Division algorithm 64
Domain of a variable 8
Domain with regular boundary 419
| Domain, of a relation 9
Domain, with almost regular boundary 424
Dual basis 82
Dual space 82
Duality 15 68
Dyad 86
Echelon matrix 104
Eigenvalue 34 258
Eigenvector 34 258
Element (of a set) 6
Elementary bilinear functionals 306
Elementary matrices 105f
Elementary row operations 103
Elliptical coordinates 566
Empty set 7
Equations of variation 513f
Equicontinuity 215
Equivalence relation 19
Equivalent directed line segments 37
Equivalent norms 132 204
Equivalent truth-functional forms 5
Euclidean norm 38 122
Euler angles 548
Euler's equation(s) 184 541 543
Existential quantification 2
Exponential function 226 228
Exterior algebra 316ff
Exterior calculus 429
Exterior differential forms 429
Exterior forms 316
Fibering 19
Finite-dimensional 28
First variation 183
Fixed-point theorem 229ff
Floor of a paving 329
Flow 381
Formal adjoint 295
Fourier coefficient 254
Fourier series 254 301ff
Fourier transform 355 357
Frame 71
Free variables 2
frequency 292
Function 10f
Function space 24
Functional dependence 175ff
Fundamental form on T*(M) 515
Fundamental solution 277
Fundamental theorem of calculus 238
Fundamental Theorem of Ordinary Differential Equations 267
Fundamental theorem, of algebra 243
Geodesic 539
Geodesic coordinates 537
Geodesic curvature 468
Geodesic polar coordinates 470
Germ of functions 138
Global solutions 269
Graph 9 162
Greatest lower bound 119
Group 15
Hamilton — Jacobi equation 563
Hamiltonian mechanics 520
Hamiltonian structure 559
Hamiltonian vector fields 519 559
Heine — Borel property 214
Hermitian symmetry 249
Hilbert space 249
Homogeneity, of a norm 121
Homogeneous equation 277 282ff
Homogeneous function 148
Homogeneous polynomial on V 145
Hyperplane 41
Idempotent 59
If ..., then ... 4
Image 10
Immersion 399
Implicit-function theorem 167 230
Inclusion (set) 7
Increasing norm on  134
Increasing sequence 207
Independent set of vectors 71f
Independent subspaces 56
Indexed collection 13
Inertia tensor 546
Infinite series 221 224ff
Infinitesimal 137
Infinitesimal generator 379 381
inhomogeneous equation 277 288ff
Initial condition 267
Injection (product) 47
Injective 12
Inner content 331
Inner paving 331
Integral, of a parametrized arc 236ff
Integration 321 336
Interior 197
Interior point 124
Intermediate-value theorem 120
Intersection 17
Invariant subspace 54 63
Inverse of a relation 9
Inverse, of a function 15
Inverse-mapping theorem 167
Isomorphism 34
Isomorphism between normed linear spaces 132
Iterated integrals 346
Jacobian determinant 159
Jacobian matrix 158f
Kepler's first law 527
Kepler's second law 524
Kepler's third law 527 532
Kernel 34
kinetic energy 521
Kronecker delta function 74
Lagrange multipliers 174
Lagrange's equations 530
Law of Cosines 41 250
Least upper bound property 119
Left inverse 14
Lemma of Du Bois-Reymond 184
Length of a curve, Riemannian manifold 401
Lie bracket 389
Lie derivative of a function 383f
Lie derivative of a linear differential form 392
Lie derivative of a vector field 385 388
Lie derivative of an exterior differential form 431 452
Lie derivative, of a density 417
Limit, of a function 116 126
Line (straight) 38
Line of nodes 548
linear combination 27
Linear combination mapping 31
Linear differential equations 276ff
Linear functionals 32 82
Linear transformation 30
Lipschitz continuity 126
Local solution 269
Locally absolutely integrable density 408
Locally absolutely integrable n-form 435
Locally uniformly Lipschitz 267
Mapping 12
Matrix 32 88
Maximal solution 269
Maximum, relative 161
Mean-value theorem 148f
Member (of a set) 6
Metric space 196
Minimal polynomial 261
Momentum 511
Momentum function of a vector field 517 (Eq. 3.6)
|
|
|
| Реклама |
|
|
|
|
|
О проекте