Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations |
| Beschreibung: | 1 Online-Ressource (XIV, 244 p) |
| ISBN: | 9783662026243 9783662026267 |
| DOI: | 10.1007/978-3-662-02624-3 |
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| 500 | |a It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Struwe, Michael |
| author_facet | Struwe, Michael |
| author_role | aut |
| author_sort | Struwe, Michael |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV042423202 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-02624-3 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662026243 9783662026267 |
| language | English |
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| spelling | Struwe, Michael Verfasser aut Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems by Michael Struwe Berlin, Heidelberg Springer Berlin Heidelberg 1990 1 Online-Ressource (XIV, 244 p) txt rdacontent c rdamedia cr rdacarrier It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s 1\p DE-604 Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 2\p DE-604 Hamiltonsches System (DE-588)4139943-2 s 3\p DE-604 https://doi.org/10.1007/978-3-662-02624-3 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 |
| spellingShingle | Struwe, Michael Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik Variationsrechnung (DE-588)4062355-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4139943-2 (DE-588)4205536-2 (DE-588)4128900-6 |
| title | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems |
| title_auth | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems |
| title_exact_search | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems |
| title_full | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems by Michael Struwe |
| title_fullStr | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems by Michael Struwe |
| title_full_unstemmed | Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems by Michael Struwe |
| title_short | Variational Methods |
| title_sort | variational methods applications to nonlinear partial differential equations and hamiltonian systems |
| title_sub | Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems |
| topic | Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik Variationsrechnung (DE-588)4062355-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Statistical Physics, Dynamical Systems and Complexity Mathematik Variationsrechnung Hamiltonsches System Nichtlineare Differentialgleichung Nichtlineare partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-3-662-02624-3 |
| work_keys_str_mv | AT struwemichael variationalmethodsapplicationstononlinearpartialdifferentialequationsandhamiltoniansystems |