|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Edwards H. — Advanced Calculus: A Differential Forms Approach |
|
|
|
| Предметный указатель |
Oriented length 19 20
Oriented volume 16—18 20
orthogonal matrices 193—194 (Ex. 5—6)
Orthogonal trajectories 277 (Ex. 3)
Parabola of safety 195 (Ex. 7)
Parameterization 44—48
Parameterization of the circle 257—258
Parametric description of domains 38—43
Partial derivatives 41
Partial derivatives, definition 142
Partition of unity, continuous 206
Partition of unity, differentiable 213 (Ex. 1) 217 220
Pi, computation of 256—260
Pi, definition 34 (Ex. 1)
Pi, represented as a simple integral 65 (Ex. 14)
Picard's iteration 246
Poincare's lemma 325
Poisson's equation 339 341 348
Poisson's integral formula 287 308—310
Polar coordinates 47 64—65
Polar coordinates, differentiation of 146—147
Polynomials 381
Potential theory 335—340
Power series, operations with 420—421 (Ex. 6—9)
Product formula for sine 402 415—417
Product of forms 89
Products (infinite) 401
Products of matrices (see Matrices)
Ptolemy's trigonometric tables 379—380 (Ex. 16)
Pullbacks of 3-forms 15—16
Pullbacks of constant forms under affine maps 20 86
Pullbacks of non-constant forms under non-affine maps 40—43 142—143
Pullbacks of non-constant forms under non-affine maps, related to Leibniz notation 460
Pullbacks of non-constant forms under non-affine maps, reviewed 190
Pullbacks, computation of 12—13
Pullbacks, geometrical significance 8—12 18
Pullbacks, origin of term 11
Quadratic forms, elliptic, hyperbolic, parabolic 177—178
Quadratic forms, origin of term 175n
Quadratic forms, positive definite 183 186—187
Rank of a differentiable map (at a point not a singularity) 139
Rank of a linear map 119 124
Rank of a system of linear equations 81
Rank of an affine map 128
Rank of the exterior powers of a matrix 130 (Ex. 2)
Rank, geometrical significance 82—83
Rank, relation to pullbacks 84
Rank, reviewed 191
Ratio Test 401
Rational numbers 359—367
Real numbers 367—375
Rearrangement of series 405 (Ex. 6—9) 409
Refinement (of a subdivision) 32
Relativity (see Special relativity)
Relaxations 238
Riemann integration 426—427
Riemann's criterion for the convergence of an integral 37 (Ex. 7)
Schwarz inequality 172
Second Derivative Test 187 (Ex. 18)
Separation of variables 273
Series (infinite) 400
Sets 461—462 467
Sexagesimal fractions 379—380 (Ex. 16 18)
Shears 9
| Simple iteration 240 (Ex. 1)
Sine, product formula for 402 415—417
Singularities of a differentiable map, definition 134 141
Singularities of a differentiable map, examples 134—139
Singularities of a differentiable map, reviewed 192
Snell's Law of Refraction 183 (Ex. 2)
Solution manifolds of a differential equation 314
Space as a term not implying three dimensions 80n
Special relativity 351—354
Spherical coordinates 45
Spherical coordinates, differentiation of 150 (Ex. 10)
Square roots 244 (Ex. 1)
Stationary points 170n
Stereographic projection 43—44 (Ex. 3) 47
Stokes' Theorem, in vector notation 266—268
Stokes' Theorem, proved when domain is a rectangle 60 67—68
Stokes' Theorem, statement 72—73
Stokes' Theorem, statement and proof 217—218 220—221
Subscript notation 77n
Successive approximations 226
Successive approximations of the inverse of a matrix 236
Successive approximations of the solution of an ordinary differential equation 246
Successive approximations of the solution of linear equations 236
Surface integrals 266
Surfaces (see also Manifolds)
Surfaces, defined by equations 41
Surfaces, defined by parameters 41
Tangent line to a curve in the plane 148 (Ex. 4)
Tangent plane to a surface in space 149 (Ex. 8)
Taylor series 234 (Ex. 1) 300
Tensors 23n
topology 321 324
Torus, as a compact, oriented surface 214 (Ex. 3)
Torus, parameterization of 49 (Ex. 7)
Torus, volume of 70 (Ex. 21(c))
Transcendental functions 383—384
Transpose of a matrix 98
Triangle inequality, for complex numbers 310 (Ex. 1)
Triangle inequality, for rational numbers 365
Triangle inequality, in Banach spaces 448
Trigonometric functions 251 (Ex. 1) 311
Uniform continuity 388
Uniform convergence 449
Uniform differentiability 389—390
Vector fields 265
Vector potential 347
Vector products (see Cross products)
Vector spaces, bases 115—117
Vector spaces, dimension 115—117
Vector spaces, examples 113—114
Vector spaces, formal definition 122—123
Vector spaces, glossary of terms 123—124
Vector spaces, informal definition 113
Vector spaces, linear maps 117—122
Vector spaces, origin of term 113n
Vector spaces, subspaces 114—115
Velocity vectors 147
Volume of an n-dimensional ball 425 (Ex. 12)
Volume, k-dimensional 197
Wallis' formula 405 (Ex. 5)
Wave equation 348
Work as the differential of potential 61 333—340
Work in a central force field 23 (Ex. 1)
Work in a constant force field 1—2
“Uncertainty” of an approximating sum 32—34
|
|
|
| Реклама |
|
|
|
|
|
О проекте