Loomis L.H., Sternberg S. — Advanced calculus :: Электронная библиотека попечительского совета мехмата МГУ

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Loomis L.H., Sternberg S. — Advanced calculus

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Название: Advanced calculus

Авторы: Loomis L.H., Sternberg S.

Аннотация:

This book is based on an honors course in advanced calculus that we gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. (from preface)

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second, revised edition

Год издания: 1989

Количество страниц: 589

Добавлена в каталог: 04.06.2005

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Предметный указатель

Monomial on V      145
Monotone sequence      207
Multi-index notation      193
Multilinear functionals      306ff
Multivector      318
NAME      7
Natural isomorphism      69 86
Negation      6
Neighborhood      137 201
Neighborhood, deleted      137
Nilpotent      50
Nonnegative transformation      257
Nonsingular      93
Norm      121
Norm metric      196
Normal distributions      355 (Ex. 13.1) 356
Normed linear space      121
nth-order equation      270ff
Null space      34
Nutation      550
One-parameter group, one-to-one      11
Open set      124 196
Or (connective)      4
Ordered basis      71
Ordered n-tuple      13
Ordered pair      9
Orthogonal      250
Orthogonal projection      253ff
Orthogonal transformation      262
Orthonormal      254
Orthonormal basis      112 254
Oscillating system      291ff
Outer content      331
Outer paving      331
Pair set      7
Parallel translation      40
Parallelogram law      251
Parametric equations (of a line)      38
Parametrized arc      146
Parseval's equation      254
Partial derivative      156f
Partial differential      153
Partition      19
Partition of unity      405
Partition of unity, subordinate to an open covering      406
Patch manifold      172
Paved function      338
Paved set      324 326
Paving      324
permutations      308
Phase angle      294
Plane      40
Poisson bracket      519
Polar coordinates      345
Polar decomposition      263
Polynomials      62 64
Positive definite      115 190
Pre-Hilbert space      249
Precession      547
Principle of mechanical similarity      532
Product norm      133
Product rule (for differentials)      155
Product vector space      43
Product, matrix      91
Projection      19 58
Projection-injection identities      47
Property      7
Pullback of exterior differential forms      392
Pullback of functions      372
Pullback of linear differential forms      392
Pullback of vector fields      384
Pullback, of densities      416
Pythagorean Theorem      41 251
Quadratic form      112
Quotation marks      7
Quotient space      54
Range of a relation      9
Range, of a linear transformation      34
Rank of a matrix      91
Rank, of a linear transformation      85
Real vector space      23f
Rectangles      323f
Regular differential equations      282 298
Regular solid      473
Relation      9
Rellick's lemma      362 (Ex. 14.30)
Resonance      294

Restricted variables      8
Restriction (of a relation)      10
Riemann metric      397
Right inverse      14 61
Rigid-body motion      544
Row space (of a matrix)      91
Row vector      93
Row-reduced echelon form      104
scalar      23
Scalar product      38 248
Schwarz inequality      125 249
Second conjugate space      83
Second difference      188
Second differential      150 186ff
Self-adjoint      257
Seminorm      125
Semiscalar product      248
Separation of variables      563f
Sequential convergence      202ff
Set      6
Shear transformation      56
Sign of a permutation      309
Signature (of a quadratic form)      113
simple harmonic motion      293
Skeleton      32
Small oscillations      551
Smooth arc      146
Sobolev's inequality      361
Solid angle      474
Span, linear      28
Spherical coordinates      345 (Ex. 11.4)
Standard basis      74
Star operator      320
State      510
Statement      1
Statement frame      1
stop function      237
Sturm — Liouville system      298
Submanifold      172 367
Subsequence      205
Subset      7
Subspace (vector)      24
Successive integration      346
Support of a differential form      425
Support of a function      336
Support, of a density      408
Surjective      12
Symmetric tensor      310
Tangent bundle      511
Tangent plane      162
Tangent space      373
Tangent vector      146 373
Tautology      5
Taylor's formula      191ff
Tensor product      305f
topology      201
Total linear momentum      528
Totally bounded      212
Trace      99
Translation      40 53
TRANSPOSE      90
Triangle inequality for norms      121
Triangle inequality, for metrics      196
Truth table      3
Truth-functional forms      5
Two-body problem      528
Two-norm      250
Undetermined coefficients      289
Uniform conditions      210ff
Uniform continuity      179 210
Uniform convergence      211
Uniform norm      123
Uniformly absolutely integrable      353
union      17
Unit set      7
Universal quantifier      1
Upper triangular      66
Variation of parameters      289
Variational principles      532
Vector analysis      457
Vector field      44
Vector space      23
Volume density of a Riemann metric      411
Volume of an immersed hypersurface      413 415
Weak sequential convergence      245
Wedge operation      316
Weierstrass approximation theorem      304

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