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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
Norm      131 293
Normal derivative      625
Normed vector space      132
Null sequence      190
Null space      292
Numbers      17
O(G)      117
o(h)      67 463
Odd      27
Onto      5
Open ball      135
Open covering      203
Open disc      138
Open in a subset      156
Open interval      24
Open neighborhood      152
Open set      51
Opposite path      398
Order of magnitude      116
Ordering      21
Oriented boundary      613
Oriented volume      584
Orthogonal      138 292
Orthogonal family      301
Orthonormal      301
Oscillation      576
Oscillatory integral      318 336
p's and q's      29 32 69 216—217
Parallelogram law      137 305
Parametrized      269
Partial derivative      275 371 495
Partial differential operator      324 406
Partial sum      206
Partition of interval      105 249
Partition of rectangle      565
Parts (summation by)      220
Path      388
path integral      398 418 438
Pathwise connected      448
Peano curve      225
Periodic      93
Permutation      5
Perpendicular      138 292
Piecewise $C^1$      389
Piecewise continuous      253 388
Point of accumulation      35 36 132 157 193
Pointwise convergence      179 317
Poisson inversion      352
Poisson kernel      315
Poisson summation formula      358
Polar coordinates      518 595
Polar form      98
Polynomials      54 287
Positive definite      133 292
Positive integer      8
Positive number      21
potential energy      390
Potential function      392
Power series      234
Prime numbers      124
PRODUCT      162
Product decomposition      526
Product of matrices      458
Products (infinite)      214
Projection      294
Proper      4
Pythagoras theorem      293
Quadratic form      413
Radius of convergence      235
Rapidly decreasing at infinity      353
Ratio Test      209
Rational number      27
Real number      17
Real part      96 99
rectangle      565
Rectangular path      433
refinement      250 566
Regulated map      253
Relatively continuous      170
Relatively uniformly continuous      199
Remainder in Taylor formula      110
Repeated integral      581
Residue      431
Riemann integrable      567
Riemann sum      106
Riemann — Lebesgue lemma      318
Riemann — Stieltjes      259
Root      56 201
Sawtooth function      345
Scalar product      133
Schanuel's theorem      217
Schwartz space      353
Schwarz inequality      135 294
Second derivative      477
Self conjugate      173
Seminorm      136
Semiparallelogram law      149
SEQUENCE      12 32
Series      206
Shrinking lemma      502
Shrinking map      503
Shub's theorem      505
simplex      620
Sine and cosine      90
Size of partition      106 570
Sphere      135 600
Spherical coordinates      599
Square root      23
Squeezing process      48
Standard      608
Star shaped      449
Step map      249 252
Stieltjes integral      259
Stirling's formula      120
Stokes' theorem      614 622
Strictly convex      72
Strictly decreasing      35 71
Strictly increasing      35 71
Strictly monotone      75
Subcovering      203
Subdivision      434
Submanifold      531
Subrectangle      566
Subsequence      13
Subset      4
subspace      130
Sufficiently close      43
Sufficiently large      35
Sum of series      206
Summation by parts      220
Sup      30
Sup norm      132 139
Support      362
Surjective      5
Symmetric second derivative      481
Tangent plane      386
Tangent vector      602
Tate's lemma      503
Taylor formula      109 408 490
Taylor polynomial      111 409
Taylor series, arbitrary      244
Theta series      358
Tietze extension      231
Total family      300
Translation      514
Trecimal expansion      192 224
Triangle inequality      131
Trigonometric degree      311
Trigonometric polynomials      306 311
Uniform convergence      179 229
Uniform distribution      310
Uniform limit      180
Uniformly Cauchy      179
Uniformly continuous      63 174 198
union      4
Unit element      9
Unit vector      295 625
Upper integral      567
Upper sum      105
Value      4
Variation      260
Vector      130
Vector field      390 538
Vector field on sphere      602
Vector space      129
Velocity      269
Volume      575 584
Volume of n-ball      598
Wallis product      121
Weakly increasing      71
Weierstrass approximation theorem      287
Weierstrass test      230
Weierstrass — Bolzano theorem      38 193
Well-ordering      8
Winding number      422
Zero      18
Zeros of ideal      205
Zeta function      359
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