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Lang S.A. — Undergraduate Analysis
Lang S.A. — Undergraduate Analysis

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Название: Undergraduate Analysis

Автор: Lang S.A.

Аннотация:

This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disk, ordinary differential equations, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises. Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of [actual symbol not reproducible]-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1997

Количество страниц: 668

Добавлена в каталог: 04.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1$      73 468
$C^1$-invertible      512
$C^p$      73 468 482 487
$C^p$ chart      514
$C^p$ coordinate system      514
$C^p$ norm      137
$C^p$-isomorphism      513
$C^{\infty}$ functions      82 244 268
$L^1$-norm      141 254 329
$L^2$-norm      141 255 299
$\ell^1$      216 233
$\ell^2$      215
Abel's theorem      220 223 239
Absolute convergence      213 229
Absolute convergence of integrals      329
Absolute convergence of series      213 229
Absolute value, complex      97
Absolute value, real      23
Absolutely integrable      329
Acceleration      269
Accumulation point      35 36 132 157
Adherent      41 153
Admissible      570 572 573
Algebraic closure      201
Alternating product      607
Anosov's theorem      511
approach      42 51 160
Approximation by step maps      252 307 319
Approximation of identity      286
Arbitrarily large      51
Arcsine      95
arctan      95 114
Area of sphere      600
Associative      17
Asymptotic      119
Asymptotic expansion      118
Ball      135
Banach space      143
Beginning point      389
Bernoulli polynomial      325
Bessel function      347 364
Big oh      117
Bijective      6
Bilinear      478
Binomial coefficients and expansion      11 89 111
Block      584
Bonnet mean value theorem      107
Bound for linear map      247 456
Boundary      159
Boundary of chain      621
Boundary point      158
Bounded      29 131 135
Bounded from above or below      29
bounded linear map      178 247
Bounded metric      136
Bounded set      29 135
Bounded variation      260
Bruhat — Tits      149 150
Bump function      81
Cantor set      224
Cauchy criterion      167
Cauchy sequence      39 143 149
Cesaro kernel      312
Cesaro summation      314
Chain      428 620
Chain rule      67 282 396 471
Change of variables      490 593
Characteristic function      574
Chart      514 531
Circumcenter      150
Class $C^p$      73 468 482 487
Close together      441 442
Closed      153
Closed ball      135
Closed chain      428
Closed in a subset      156
Closed interval      24
Closed rectangle      565
Closure      155 157
Coefficients      56 235
Commutative      18
Commute with limits      61
Compact      193
Comparison Test      209
Complement      4
complete      143
Completeness axiom      29
Completion      189 192
complex numbers      95
Composite      6 164
conjugate      96
Connected      389
Connected along a partition      419
Conservation law      391
Conservative      390
Constant term      56
Contained      4
continuous      59 156 170
Continuous linear map      178 246 455
Continuous path      388
Converge      34 39 143 149 206 327
Converge absolutely      213 224 225 229
Converge uniformly      179
convergence of integrals      327
Convergence of products      214
Convex      64 65 72
Convolution      283 311 355
Coordinate function      172 472
Coordinate system      514
Cover      203
Critical point      546
cube      579
Curve      268
Curve integral      395 418 438
Dampened oscillation      219
Decimal expansion      214
Decomposable form      608
Decreasing      36 71
Degree      56 201
Degree of differential operator      374
Dense      155
Denumerable      11
Dependence on initial conditions      557
Derivation      410
Derivative      66 99 268
Differentiable      66 73 380 382 463 465
Differential equations      538
Differential form      608
Differential operator      374
Differentiating series      241
Differentiating under integral sign      276 336 500
Dirac family      347
Dirac sequence      284 313
Directional derivative      383
Dirichlet kernel      311
Disc      138
Distance      25 135 176
Distance function      135
Distributive      19
diverge      209
Domain of flow      545
Dual space      608
Eigenfunction      306
Eigenvector      413
Element      3
Elkies estimate      325
Empty      3
End point      389
enumerate      11
Equidistribution      310
Equivalence relation      15 32
Equivalent norms      135
Euclidean norm      137
Euler number      89
Euler's relation      387
Even      27
Exact form      613
Exponential      78
Exponential of matrices      509
Extend by continuity      172 176
Extension theorem for linear maps      247
Exterior derivative      610
Family      183
Family of open sets      203
Fejer kernel      312
finite      12
Finite sequence      12
Finite subcovering      203
Fixed point theorem      150 502
Flow      541
Formal linear combination      630
Fourier coefficients      294 295
Fourier series      296 303
Fourier transform      342 354
Free homotopy      452
Function      41
Functional equations      358
Fundamental lemma of integration      265
Fundamental solution of heat equation      349
Gamma function      346
Generate vector space      130
Global flow      544
Gradient      380
Graph      41
Greatest lower bound (glb)      30
Green's function      378
Green's theorem      624
Half-closed      24
Half-open      24
Harmonic      316 375
Heat equation      350
Heat kernel      348 372
Heat operator      349
Hermitian product      291
hessian      486
Homologous      425 429
Homotopic      444
Homotopy      444
Homotopy relative to end points      448
Hyperbolic      510
Hyperplane      385
Hypersurface      411
Ideal of continuous functions      205
identity map      6
Image      4
Imaginary part      96 99
Implicit functions      522 527
Improper integral      326
In verse image of a form      616
Increasing      35 71
Indefinite integral      103
Induction      8
inf      30
Infinite      12
Infinite interval      24
infinity      50
Initial condition      538 557
Injective      5
Integers      27
Integrability theorem      430
Integrable      471
integral      101 249 395 568
Integral along a path      418 438
Integral curve      538
Integral equation      504 510
Integral mean value theorem      107
Integral operator      285 290 306
Integral test      210
Integration by parts      105
Integration of series      239
Interchange of derivative and integral      276 337 340
Interchange of integrals      277 339 342
Interchange of limits      185
Interior point      158
Intermediate Value Theorem      62
Intersection      4
interval      24
Inverse      74 96
Inverse image      156
Inverse mapping      7
Inverse mapping theorem      502 515
Inverse path      398
Inversion function      74
Invertible      76 512
Invertible linear map      506
Irrational      28
Isolated      158 161
Isometry      150
Isomorphism      76
Jacobian      467
Jacobian determinant      589
Kernel function      286
Khintchine Theorem      216
kinetic energy      391
Lagrange multiplier      412
Landau kernel      288
Laplace operator      316
Lattice point problem      366
Leading coefficient      56
Least upper bound (lub)      29
Lebesgue integral      262
Length      293
Level surface      384
Li(x)      123
LIMIT      41 42 50 143 160
Limit inferior      41
Limit superior      40
linear combination      130
Linear differential equation      552
Lipschitz condition      74 174 320 540 578
Lipschitz constant      74 540
Little oh      117
Local flow      541
Local isomorphism      513
Locally integrable      418 438
Locally invertible      513
Logarithm      83 133
Lower integral      567
Lower sum      105
Mapping      4
Matrix representing bilinear map      483
Maximum      61
Mean value theorem      71 475
Measure      262
Measure less than epsilon      263
Measure zero      215 577
Metric space      136
midpoint      149
Minimum      61
Monotone      76
Multilinear      478
Multiple integral      568 581
Multiplication      18
Natural numbers      3 8
Negative      22
Negligible      569
Newton quotient      66
Newton's law      390
Newton's method      504
Non-degenerate block      584
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