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Browder A. — Mathematical Analysis: An Introduction
Browder A. — Mathematical Analysis: An Introduction

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Название: Mathematical Analysis: An Introduction

Автор: Browder A.

Аннотация:

Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 370

Добавлена в каталог: 11.12.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L(\mu)$      225
$L^{p}(\mu)$      235
$L^{p}(\mu)$, completeness of      237
$T^{r}$ (tensors of rank r)      270
$\Delta$ (Laplace operator)      314
$\delta^{i}_{j}$      (see Kronecker $\delta$)
$\delta^{K}_{J}$      (see Kronecker $\delta$)
$\epsilon$-net      143
$\epsilon(\sigma)$      (see Sign of permutation)
$\lambda$-System      237
$\Lambda^{r}$ (alternating tensors of rank r)      272
$\mu^{*}$-measurable      211
$\pi$-system      237
$\sigma$-algebra      204 238
$\sigma$-algebra, generated by      205
$\sigma$-field      221
$\varepsilon^{K}_{J}$      (see Kronecker epsilon)
A.a.      (see Almost all)
a.e      (see Almost everywhere)
Abel, N      53 72
Absolutely convergent, integral      116
Absolutely convergent, series      40
Additive, countably      206
Additive, finitely      203
Adjoint map      280
Agnesi, M      96
Alexandroff, P      153
Algebra of sets      202
Algebra, generated by      205
Almost all      221 226
Almost everywhere      226
Alternating tensor      272
Alternating tensors in $R^3$      279
Alternating tensors, basis for      276
Alternating tensors, dimension of      276
Alternation operator      275
Ampere, A.M      321
Antiderivative      110
Antisymmetry      273
Arbogast, L      95
Archimedean property      15
Archimedes      26 95
Arzela, C      154
Arzela- Ascoli theorem      145 146
Ascoli, G      154
Axiom of Choice      217 218
Baire theorem      136
Baire, R      153
Ball      128
Barrow, I      122
Basis      176
Bernoulli, Jakob      53 121
Bernoulli, Johann      96
Bernstein, S      174
Bijective      3
Bolzano — Weierstrass property      144
Bolzano — Weierstrass theorem      35
Bolzano, B      53 72 153
Bonnet, O      96
Borel Cantelli lemma      222
Borel measure, translation invariant, uniqueness of      239
Borel, algebra      205
Borel, E      202 221
Borel, measure      206
Borel, set      205 214 215 220 224
Bound, lower      13
Bound, upper      13
Boundary      125
Boundary of manifold      256
Bounded      142
Bounded, totally      142
Brouwer. L.E.J      321
Bunyakovsky. V      109
Cantor function      248
Cantor set      149 201 248
Cantor set, dimension of      211
Cantor set, measure of      213
Cantor, G.      26 27 153 174
Cardinality      6
Cartan, E.      284
Cartesian product      2 133
Cauchy condensation test      43
Cauchy sequence      36 237
Cauchy. A.      72 96 121 122
Chain rule      82 184
Change of variables, linear      240
Change of variables, smooth      112 241
Class $C^\infty$      190
Classical notation      187
Closed      124
Closed ball      257
Closure      125
Column vector      177
Compact      140 215
Compact, relatively      144
Compact, sequentially      144
Complement      2
Complement, relative      1
complete      236
Complete, metric space      130
Complete, ordered field      14
Component      148
Condensation point      150
Conjugate space      269
Connected      147 186
Connected component      148
Connected set, continuous image      148
Content      121
Continued fraction      36 39
Continuity from below      206
Continuous function      57
Continuous image of      141
Continuous map      126
Contraction map      137 193
Convergence in measure      249
Convergence, almost everywhere      249
Convergence, mean square      166
Convergence, monotone      225
Convergence, pointwise      62 226 229
Convergence, uniform      62 226
Convex coordinate patch      293
Convex function      70 78
Convex set      185 250
Convolution      251
Coordinate patch      255
Coset      218
cosets      277
Countable      6 8
Countable additivity      219
Countable base      131
Countable subadditivity      219
Countably additive      206
Countably infinite      6
Countably subadditive      209
Covector      269 283
Cramer's rule      181
Critical point      251
Critical value      251
Cross product      289
cube      242
Curl      289
Curve      253
Cut-off function      299
Daniell, P.J      252
Darboux, G      84 96
De Rham cohomology      291
Dedekind, R      21 26
Deformation      262
DeMorgan’s laws      2 212
Dense      16 126 218 220
Derivative      74 182
Derivative of convex function      80 81
Derivative of exponential      77
Derivative of polynomial      76
Derivative of trigonometric function      77
Derivative, directional      197
Derivative, higher order      88
Determinant      181 275
Determinant, Jacobian      182
Diagonal matrix      240
Diameter      142
Diffeomorphism      254
Differentiable      74 182 254
Differential      76 182 261
Differential calculus      81
Differential form      285
Differential form, closed      291
Differential form, exact      291
Differential of form      (see Exterior differential)
Differentiation of series      114
Dini, U      73
Dini’s theorem      64
Dirichlet principle      317
Dirichlet test for integrals      117
Dirichlet test for series      43
Dirichlet, P.G.L      53 72 174
Dirichlet’s Theorem      16 218
Disconnected      147
Disconnected, totally      149
Distribution function      248 251
Divergence      288
Divergence theorem      312
Domain      3
Dominated Convergence Theorem      230
Dual basis      270 282
Dual space      269
Dummy variable      245
Dynkin’s $\pi- \lambda$ theorem      238
e      33 66
Einstein, A      296
Empty set      2
Equicontinuous      145
Equivalence classes      2 217 236
Eudoxus      26
Euler, L      53 73 96
Euler’s constant      113
Expansion, binary      31
Expansion, continued fraction      38
Expansion, decimal      31
Exterior differential      287
Exterior product      277
Exterior product, (anti)commutativity of      279
Exterior product, associativity of      278
Fatou’s Lemma      230 248
Fermat, P      121
Fibonacci numbers      54
Field      10 13
Field of sets      221
Field, ordered      12
Finite induction      4
Finite intersection property      151
Finitely additive      219
Fixed point theorem, Brouwer      305 307
Fixed point theorem, contraction map      137
Fourier coefficients      164
Fourier coefficients, uniqueness of      165
Fourier series      164
Fourier, J      121
Frechet derivative      182
Frechet, M      153 182 221
Fubini Tonelli theorem      245—247
Fubini. G.      252
Function      3 16
Function, absolute value      17
Function, Borel      226
Function, Borel measurable      244
Function, characteristic      225
Function, complex      96
Function, continuous      55 57
Function, convex      70 78 96 233 250
Function, Dirichlet      56 100
Function, exponential      65—66
Function, graph of      3 251
Function, greatest integer      58
Function, harmonic      314
Function, indicator      225
Function, inverse      85
Function, Lebesgue      226
Function, limit of      55
Function, logarithm      66
Function, lower semicontinuous      151
Function, measurable      223
Function, monotone      56
Function, nowhere differentiable continuous      75
Function, periodic      162
Function, piecewise linear      61
Function, polynomial      17 58
Function, radial      320
Function, rational      17 58
Function, sign      17
Function, simple      225—228 232
Function, step      232
Function, trigonometric      66—69
Function, uniformly continuous      61
Function, upper semicontinuous      70 151
Fundamental theorem of calculus      110 111
Gauss, C.F      54 121 267
Geodesics      161
Gradient      288
Gram determinant      308
Graph      256
Grassman, H      283
Green, G      321
Green’s identities      314
Group      273
Hahn, H      221
Halmos, P      25
Hardy, G.H      27
Harmonic function      314 318
Hausdorff, dimension      211
Hausdorff, F      153 154 211
Hausdorff, measure      210
Hausdorff, space      135
Heine — Borel theorem      140 144 210
Heine, H.E      72
Hermite, C      27
Herstein, I      27
Holder, O      252
Homeomorphic      127
Homeomorphism      127
Hypersurface      265 312
IJrysohn, P      153
Image      3 178
Implicit function theorem      194 259
Implicit function theorem, classical notation      196
incommensurability      8
Indexed family      4
Induced mapping of forms      290—291
Inequality, arithmetic-geometric means      234
Inequality, Bernoulli      30
Inequality, Bessel      168
Inequality, Bunyakovsky      (see Schwarz)
Inequality, Cauchy      129
Inequality, Cauchy — Schwarz — Bunyakovsky      235
Inequality, Chebyshev      233
Inequality, Holder      235
Inequality, Jensen      233
Inequality, Liapounov      234
Inequality, Minkowski      235
Inequality, Schwarz      108 165
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