A History of the Calculus of Variations from the 17th through the 19th Century:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1980
|
| Schriftenreihe: | Studies in the History of Mathematics and Physical Sciences
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathematicians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861 |
| Beschreibung: | 1 Online-Ressource (410p) |
| ISBN: | 9781461381068 9781461381082 |
| ISSN: | 0172-570X |
| DOI: | 10.1007/978-1-4613-8106-8 |
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| 500 | |a The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathematicians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861 | ||
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Datensatz im Suchindex
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| author | Goldstine, Herman H. |
| author_facet | Goldstine, Herman H. |
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| ctrlnum | (OCoLC)863787701 (DE-599)BVBBV042420662 |
| 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 | 10.1007/978-1-4613-8106-8 |
| era | Geschichte 1600-1900 gnd |
| era_facet | Geschichte 1600-1900 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461381068 9781461381082 |
| issn | 0172-570X |
| language | English |
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| series | Studies in the History of Mathematics and Physical Sciences |
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| spelling | Goldstine, Herman H. Verfasser aut A History of the Calculus of Variations from the 17th through the 19th Century by Herman H. Goldstine New York, NY Springer New York 1980 1 Online-Ressource (410p) txt rdacontent c rdamedia cr rdacarrier Studies in the History of Mathematics and Physical Sciences 5 0172-570X The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathematicians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861 Geschichte 1600-1900 gnd rswk-swf Mathematics Global analysis (Mathematics) Analysis Mathematik Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Geschichte 1600-1900 z 1\p DE-604 Studies in the History of Mathematics and Physical Sciences 5 (DE-604)BV000003995 5 https://doi.org/10.1007/978-1-4613-8106-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldstine, Herman H. A History of the Calculus of Variations from the 17th through the 19th Century Studies in the History of Mathematics and Physical Sciences Mathematics Global analysis (Mathematics) Analysis Mathematik Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | A History of the Calculus of Variations from the 17th through the 19th Century |
| title_auth | A History of the Calculus of Variations from the 17th through the 19th Century |
| title_exact_search | A History of the Calculus of Variations from the 17th through the 19th Century |
| title_full | A History of the Calculus of Variations from the 17th through the 19th Century by Herman H. Goldstine |
| title_fullStr | A History of the Calculus of Variations from the 17th through the 19th Century by Herman H. Goldstine |
| title_full_unstemmed | A History of the Calculus of Variations from the 17th through the 19th Century by Herman H. Goldstine |
| title_short | A History of the Calculus of Variations from the 17th through the 19th Century |
| title_sort | a history of the calculus of variations from the 17th through the 19th century |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Variationsrechnung |
| url | https://doi.org/10.1007/978-1-4613-8106-8 |
| volume_link | (DE-604)BV000003995 |
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