Cauchy and the creation of complex function theory:
Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathemat...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1997
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| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book makes use of the whole spectrum of available original sources; it will be recognised as the authoritative work on the creation of complex function theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (216 pages) |
| ISBN: | 9780511551697 |
| DOI: | 10.1017/CBO9780511551697 |
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| 520 | |a Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book makes use of the whole spectrum of available original sources; it will be recognised as the authoritative work on the creation of complex function theory | ||
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| author | Smithies, F. 1912- |
| author_facet | Smithies, F. 1912- |
| author_role | aut |
| author_sort | Smithies, F. 1912- |
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| bvnumber | BV043945283 |
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| collection | ZDB-20-CBO |
| contents | Background to Cauchy's work on complex function theory Cauchy's 1814 memoir on definite integrals Miscellaneous contributions (1815-1825) 1825 memoir and associated articles Calculus of residues Lagrange series and the Turin memoirs Summary and conclusions |
| ctrlnum | (ZDB-20-CBO)CR9780511551697 (OCoLC)849998626 (DE-599)BVBBV043945283 |
| dewey-full | 515/.9/092 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9/092 |
| dewey-search | 515/.9/092 |
| dewey-sort | 3515 19 292 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511551697 |
| era | Geschichte 1800-1900 |
| era_facet | Geschichte 1800-1900 |
| format | Electronic eBook |
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| id | DE-604.BV043945283 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:23Z |
| institution | BVB |
| isbn | 9780511551697 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029354253 |
| oclc_num | 849998626 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (216 pages) |
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| publishDate | 1997 |
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| publisher | Cambridge University Press |
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| spelling | Smithies, F. 1912- Verfasser aut Cauchy and the creation of complex function theory Frank Smithies Cauchy & the Creation of Complex Function Theory Cambridge Cambridge University Press 1997 1 online resource (216 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1 Background to Cauchy's work on complex function theory 2 Cauchy's 1814 memoir on definite integrals 3 Miscellaneous contributions (1815-1825) 4 1825 memoir and associated articles 5 Calculus of residues 6 Lagrange series and the Turin memoirs 7 Summary and conclusions Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book makes use of the whole spectrum of available original sources; it will be recognised as the authoritative work on the creation of complex function theory Cauchy, Augustin Louis / Baron / 1789-1857 Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd rswk-swf Geschichte 1800-1900 Geschichte Functions of complex variables / History / 19th century Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 p Funktionentheorie (DE-588)4018935-1 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-06887-1 Erscheint auch als Druckausgabe 978-0-521-59278-9 https://doi.org/10.1017/CBO9780511551697 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Smithies, F. 1912- Cauchy and the creation of complex function theory Background to Cauchy's work on complex function theory Cauchy's 1814 memoir on definite integrals Miscellaneous contributions (1815-1825) 1825 memoir and associated articles Calculus of residues Lagrange series and the Turin memoirs Summary and conclusions Cauchy, Augustin Louis / Baron / 1789-1857 Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd Geschichte Functions of complex variables / History / 19th century Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)118519735 (DE-588)4018935-1 |
| title | Cauchy and the creation of complex function theory |
| title_alt | Cauchy & the Creation of Complex Function Theory Background to Cauchy's work on complex function theory Cauchy's 1814 memoir on definite integrals Miscellaneous contributions (1815-1825) 1825 memoir and associated articles Calculus of residues Lagrange series and the Turin memoirs Summary and conclusions |
| title_auth | Cauchy and the creation of complex function theory |
| title_exact_search | Cauchy and the creation of complex function theory |
| title_full | Cauchy and the creation of complex function theory Frank Smithies |
| title_fullStr | Cauchy and the creation of complex function theory Frank Smithies |
| title_full_unstemmed | Cauchy and the creation of complex function theory Frank Smithies |
| title_short | Cauchy and the creation of complex function theory |
| title_sort | cauchy and the creation of complex function theory |
| topic | Cauchy, Augustin Louis / Baron / 1789-1857 Cauchy, Augustin Louis 1789-1857 (DE-588)118519735 gnd Geschichte Functions of complex variables / History / 19th century Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Cauchy, Augustin Louis / Baron / 1789-1857 Cauchy, Augustin Louis 1789-1857 Geschichte Functions of complex variables / History / 19th century Funktionentheorie |
| url | https://doi.org/10.1017/CBO9780511551697 |
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