Elements of Mathematics Functions of a Real Variable: Elementary Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc |
| Beschreibung: | 1 Online-Ressource (XIV, 338 p) |
| ISBN: | 9783642593154 9783642639326 |
| DOI: | 10.1007/978-3-642-59315-4 |
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| 245 | 1 | 0 | |a Elements of Mathematics Functions of a Real Variable |b Elementary Theory |c by Nicolas Bourbaki, Philip Spain |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 2004 | |
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| 500 | |a This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Real Functions | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Spain, Philip |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Bourbaki, Nicolas |
| author_facet | Bourbaki, Nicolas |
| author_role | aut |
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| building | Verbundindex |
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| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863775452 (DE-599)BVBBV042422755 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-59315-4 |
| format | Electronic eBook |
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| id | DE-604.BV042422755 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642593154 9783642639326 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858172 |
| oclc_num | 863775452 |
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| physical | 1 Online-Ressource (XIV, 338 p) |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Bourbaki, Nicolas Verfasser aut Elements of Mathematics Functions of a Real Variable Elementary Theory by Nicolas Bourbaki, Philip Spain Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XIV, 338 p) txt rdacontent c rdamedia cr rdacarrier This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc Mathematics Real Functions Mathematik Spain, Philip Sonstige oth https://doi.org/10.1007/978-3-642-59315-4 Verlag Volltext |
| spellingShingle | Bourbaki, Nicolas Elements of Mathematics Functions of a Real Variable Elementary Theory Mathematics Real Functions Mathematik |
| title | Elements of Mathematics Functions of a Real Variable Elementary Theory |
| title_auth | Elements of Mathematics Functions of a Real Variable Elementary Theory |
| title_exact_search | Elements of Mathematics Functions of a Real Variable Elementary Theory |
| title_full | Elements of Mathematics Functions of a Real Variable Elementary Theory by Nicolas Bourbaki, Philip Spain |
| title_fullStr | Elements of Mathematics Functions of a Real Variable Elementary Theory by Nicolas Bourbaki, Philip Spain |
| title_full_unstemmed | Elements of Mathematics Functions of a Real Variable Elementary Theory by Nicolas Bourbaki, Philip Spain |
| title_short | Elements of Mathematics Functions of a Real Variable |
| title_sort | elements of mathematics functions of a real variable elementary theory |
| title_sub | Elementary Theory |
| topic | Mathematics Real Functions Mathematik |
| topic_facet | Mathematics Real Functions Mathematik |
| url | https://doi.org/10.1007/978-3-642-59315-4 |
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