Analysis: 1
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Delhi
Hindustan Book Agency
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Texts and readings in mathematics
37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 347 S. |
| ISBN: | 9788185931944 |
Internformat
MARC
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| 100 | 1 | |a Tao, Terence |d 1975- |e Verfasser |0 (DE-588)132190370 |4 aut | |
| 245 | 1 | 0 | |a Analysis |n 1 |c Terence Tao |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Delhi |b Hindustan Book Agency |c 2009 | |
| 300 | |a XVI, 347 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts and readings in mathematics |v 37 | |
| 490 | 0 | |a Texts and readings in mathematics |v ... | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a QA 299.6-302 Analysis-general | |
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| 830 | 0 | |a Texts and readings in mathematics |v 37 |w (DE-604)BV011380811 |9 37 | |
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Datensatz im Suchindex
| _version_ | 1804145676366381056 |
|---|---|
| adam_text | Contents
Preface
to the first edition
xi
Preface to the second edition
xvii
1
Introduction
1
1.1
What is analysis?
....................... 1
1.2
Why do analysis .
....................... 2
2
Starting at the beginning: the natural numbers
13
2.1
The
Pernio
axioms
...................... 15
2.2
Addition
............................ 24
2.3
Multiplication
......................... 29
3
Set theory
33
3.1
Fundamentals
......................... 33
3.2
Russell s paradox (Optional)
................ 46
3.3
Functions
........................... 49
3.4
Images and inverse images
.................. 56
3.5
Cartesian products
...................... 62
3.6
Cardinality of sets
...................... 67
4
Integers and rationals
73
4.1
The integers
.......................... 73
4.2
The rationals
......................... 80
4.3
Absolute value and exponentiation
............. 85
4.4
Gaps in the rational numbers
................ 89
5
The real numbers
93
5.1
Cauchy sequences
....................... 95
5.2
Equivalent Cauchy sequences
................ 99
5.3
The construction of the real numbers
............ 101
5.4
Ordering the reals
......................
HO
yjij Contents
5.5
The least upper bound property
..............115
5.6
Real exponentiation, part I
.................120
6
Limits of sequences
125
6.1
Convergence and limit laws
.................125
6.2
The Extended real number system
.............132
6.3
Suprema
and
Infima
of sequences
..............136
6.4
Limsup, Liminf. and limit points
..............138
6.5
Some standard limits
.....................147
6.6
Subsequences
.........................148
6.7
Real exponentiation, part II
.................151
7
Series
154
7.1
Finite series
..........................154
7.2
Infinite series
.........................163
7.3
Sums of non-negative numbers
...............169
7.4
Rearrangement of series
................... 173
7.5
The root and ratio tests
...................177
8
Infinite sets
180
8.1
Countability
..........................180
8.2
Summation on infinite sets
..................187
8.3
Uncountable sets
.......................194
8.4
The axiom of choice
.....................197
8.5
Ordered sets
..........................201
9
Continuous functions on
R
210
9.1
Subsets of the real line
....................210
9.2
The algebra of real-valued functions
............216
9.3
Limiting values of functions
.................219
9.4
Continuous functions
.....................226
9.5
Left and right limits
.....................230
9.6
The maximum principle
...................233
9.7
The intermediate value theorem
...............237
9.8
Monotonie
functions
.....................240
9.9
Uniform continuity
......................242
9.10
Limits at infinity
.......................248
10
Differentiation of functions
250
10.1
Basic definitions
.......................250
Contents ix
10.2
Local maxima, local minima, and derivatives
.......256
10.3
Monotone functions and derivatives
.............259
10.4
Inverse functions and derivatives
..............260
10.5
ĽHôpitaľs
rule
........................263
11
The Riemann integral
266
11.1
Partitions
...........................267
11.2
Piecewise constant functions
.................271
11.3
Upper and lower Riemann integrals
.............275
11.4
Basic properties of the Riemann integral
..........279
11.5
Riemann integrability of continuous functions
.......284
11.6
Riemann integrability of monotone functions
.......288
11.7
A non-
Riemann
integrable
function
.............290
11.8
The Riemann-Stieltjes integral
...............291
11.9
The two fundamental theorems of calculus
.........294
ll.lOConsequences of the fundamental theorems
........299
A Appendix: the basics of mathematical logic
304
A.I Mathematical statements
..................305
A.2 Implication
..........................311
A.3 The structure of proofs
....................316
A.4 Variables and quantifiers
...................319
A.5 Nested quantifiers
......................323
A.
6
Some examples of proofs and quantifiers
..........326
A.7 Equality
............................328
В
Appendix: the decimal system
330
B.I The decimal representation of natural numbers
......331
B.2 The decimal representation of real numbers
........334
Index
339
|
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| id | DE-604.BV037388252 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:23:14Z |
| institution | BVB |
| isbn | 9788185931944 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022541199 |
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| physical | XVI, 347 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Hindustan Book Agency |
| record_format | marc |
| series | Texts and readings in mathematics |
| series2 | Texts and readings in mathematics |
| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Analysis 1 Terence Tao 2. ed. New Delhi Hindustan Book Agency 2009 XVI, 347 S. txt rdacontent n rdamedia nc rdacarrier Texts and readings in mathematics 37 Texts and readings in mathematics ... Mathematical analysis QA 299.6-302 Analysis-general (DE-604)BV022931971 1 Texts and readings in mathematics 37 (DE-604)BV011380811 37 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022541199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Analysis Texts and readings in mathematics Mathematical analysis QA 299.6-302 Analysis-general |
| title | Analysis |
| title_auth | Analysis |
| title_exact_search | Analysis |
| title_full | Analysis 1 Terence Tao |
| title_fullStr | Analysis 1 Terence Tao |
| title_full_unstemmed | Analysis 1 Terence Tao |
| title_short | Analysis |
| title_sort | analysis |
| topic | Mathematical analysis QA 299.6-302 Analysis-general |
| topic_facet | Mathematical analysis QA 299.6-302 Analysis-general |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022541199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022931971 (DE-604)BV011380811 |
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