Analysis: 2
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Delhi
Hindustan Book Agency
2014
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Texts and readings in mathematics
38 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 218 S. |
| ISBN: | 9789380250656 |
Internformat
MARC
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| 245 | 1 | 0 | |a Analysis |n 2 |c Terence Tao |
| 250 | |a 3. ed. | ||
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| 300 | |a XIV, 218 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Texts and readings in mathematics |v 38 | |
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Datensatz im Suchindex
| _version_ | 1804174795701485568 |
|---|---|
| adam_text | Contents^
Preface to the first edition lx
Preface to the second and third editions xv
1 Metric spaces 1
1.1 Definitions and examples............................. 1
1.2 Some point-set topology of metric spaces.............10
1.3 Relative topology....................................15
1.4 Cauchy sequences and complete metric spaces..........17
1.5 Compact metric spaces................................21
2 Continuous functions on metric spaces 28
2.1 Continuous functions...................................28
2.2 Continuity and product spaces..........................31
2.3 Continuity and compactness.............................34
2.4 Continuity and connectedness...........................36
2.5 Topological spaces (Optional) .........................39
3 Uniform convergence 45
3.1 Limiting values of functions ......................... 46
3.2 Pointwise and uniform convergence......................48
3.3 Uniform convergence and continuity.....................53
3.4 The metric of uniform convergence .....................56
3.5 Series of functions; the Weierstrass M-test.......■ * 58
3.6 Uniform convergence and integration....................61
3.7 Uniform convergence and derivatives ...................63
3.8 Uniform approximation by polynomials...................66
4 Power series 75
4.1 Formal power series....................................75
4.2 Real analytic functions................................78
viii Contents
4.3 Abel’s theorem......................................... 83
4.4 Multiplication of power series ..........................87
4.5 The exponential and logarithm functions..................90
4.6 A digression on complex numbers..........................93
4.7 Trigonometric functions.................................101
5 Fourier series 107
5.1 Periodic functions......................................108
5.2 Inner products on periodic functions....................110
5.3 Trigonometric polynomials...............................114
5.4 Periodic convolutions...................................116
5.5 The Fourier and Plancherel theorems.....................121
6 Several variable differential calculus 127
6.1 Linear transformations . ...............................127
6.2 Derivatives in several variable calculus ...............134
6.3 Partial and directional derivatives.....................137
6.4 The several variable calculus chain rule................144
6.5 Double derivatives and Clairaut’s theorem...............147
6.6 The contraction mapping theorem.........................149
6.7 The inverse function theorem in several variable calculus 152
6.8 The implicit function theorem...........................157
7 Lebesgue measure 162
7.1 The goal: Lebesgue measure..............................164
7.2 First attempt: Outer measure............................166
7.3 Outer measure is not additive...........................174
7.4 Measurable sets.........................................176
7.5 Measurable functions....................................183
8 Lebesgue integration 187
8.1 Simple functions........................................187
8.2 Integration of non-negative measurable functions........193
8.3 Integration of absolutely integrable functions..........201
8.4 Comparison with the Riemann integral....................205
8.5 Fubini’s theorem........................................207
Index
213
|
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| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV042620692 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:06:04Z |
| institution | BVB |
| isbn | 9789380250656 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028053407 |
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| physical | XIV, 218 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Hindustan Book Agency |
| record_format | marc |
| series | Texts and readings in mathematics |
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| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Analysis 2 Terence Tao 3. ed. New Delhi Hindustan Book Agency 2014 XIV, 218 S. txt rdacontent n rdamedia nc rdacarrier Texts and readings in mathematics 38 Texts and readings in mathematics ... (DE-604)BV022931971 2 Texts and readings in mathematics 38 (DE-604)BV011380811 38 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028053407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Analysis Texts and readings in mathematics |
| title | Analysis |
| title_auth | Analysis |
| title_exact_search | Analysis |
| title_full | Analysis 2 Terence Tao |
| title_fullStr | Analysis 2 Terence Tao |
| title_full_unstemmed | Analysis 2 Terence Tao |
| title_short | Analysis |
| title_sort | analysis |
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