Undergraduate Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1997
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises |
| Beschreibung: | 1 Online-Ressource (XV, 642 p) |
| ISBN: | 9781475726985 9781441928535 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4757-2698-5 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Lang, Serge |
| author_facet | Lang, Serge |
| author_role | aut |
| author_sort | Lang, Serge |
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| building | Verbundindex |
| bvnumber | BV042421369 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863899316 (DE-599)BVBBV042421369 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2698-5 |
| edition | Second Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
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| isbn | 9781475726985 9781441928535 |
| issn | 0172-6056 |
| language | English |
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| spelling | Lang, Serge Verfasser aut Undergraduate Analysis by Serge Lang Second Edition New York, NY Springer New York 1997 1 Online-Ressource (XV, 642 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 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 disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises Mathematics Global analysis (Mathematics) Analysis Mathematik Katze (DE-588)4030046-8 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf 1\p (DE-588)4006604-6 Bilderbuch gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content 3\p (DE-588)4123623-3 Lehrbuch gnd-content Analysis (DE-588)4001865-9 s 4\p DE-604 Katze (DE-588)4030046-8 s 5\p DE-604 Infinitesimalrechnung (DE-588)4072798-1 s 6\p DE-604 Algebra (DE-588)4001156-2 s 7\p DE-604 https://doi.org/10.1007/978-1-4757-2698-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge Undergraduate Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik Katze (DE-588)4030046-8 gnd Algebra (DE-588)4001156-2 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
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| title | Undergraduate Analysis |
| title_auth | Undergraduate Analysis |
| title_exact_search | Undergraduate Analysis |
| title_full | Undergraduate Analysis by Serge Lang |
| title_fullStr | Undergraduate Analysis by Serge Lang |
| title_full_unstemmed | Undergraduate Analysis by Serge Lang |
| title_short | Undergraduate Analysis |
| title_sort | undergraduate analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Katze (DE-588)4030046-8 gnd Algebra (DE-588)4001156-2 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Katze Algebra Infinitesimalrechnung Bilderbuch Aufgabensammlung Lehrbuch |
| url | https://doi.org/10.1007/978-1-4757-2698-5 |
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