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Ernst Zermelo - Collected Works/Gesammelte Werke II: Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik 2013 ed. [Kõva köide]

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  • Formaat: Hardback, 781 pages, kõrgus x laius: 235x155 mm, kaal: 1322 g, XXIX, 781 p., 1 Hardback
  • Sari: Schriften der Mathematisch-naturwissenschaftlichen Klasse 23
  • Ilmumisaeg: 10-Sep-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540708553
  • ISBN-13: 9783540708551
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Ernst Zermelo - Collected Works/Gesammelte Werke II: Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik 2013 ed.Suurem pilt
  • Formaat: Hardback, 781 pages, kõrgus x laius: 235x155 mm, kaal: 1322 g, XXIX, 781 p., 1 Hardback
  • Sari: Schriften der Mathematisch-naturwissenschaftlichen Klasse 23
  • Ilmumisaeg: 10-Sep-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540708553
  • ISBN-13: 9783540708551
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783540708551.html
Märksõnad:
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice.  However, his papers also include pioneering work in applied mathematics and mathematical physics.





This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelos work on the calculus of variations, applied mathematics, and physics.



The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.

Arvustused

From the book reviews:

This is the second and final volume of a complete edition of Ernst Zermelos collected works. This second volume covers his contributions to the calculus of variations and to applied mathematics and physics. There is much to be learned from this volume, even for those whose only interest is in Ernst Zermelo the set theorist. (J. M. Plotkin, Mathematical Reviews, July, 2014)

This is the only authoritative version of Zermelos collected works with English translations. Therefore, it is a tour de force for anyone not only interested in Zermelos papers, but also the historical background of many research areas of applied mathematics. I highly recommend this volume to applied mathematicians, from advanced undergraduate students up to specialists, such as those of variational problems and functional analysis. (Arturo Ortiz-Tapia, Computing Reviews, June, 2014)

Ernst Zermelo's curriculum vitae 1(9)
Heinz-Dieter Ebbinghaus
Zermelo 1894
Introductory note to 1894
10(16)
Craig G. Fraser
Untersuchungen zur Variations-Rechnung
26(1)
Investigations in the calculus of variations
27(161)
Zermelo 1896a
Introductory note to 1896a, 1896b, and Boltzmann 1896, 1897
188(26)
Jos Uffink
Ueber einen Satz der Dynamik und die mechanische Warmetheorie
214(1)
On a theorem of dynamics and the mechanical heat theory
215(13)
Boltzmann 1896
Introductory note: see under Zermelo 1896a Entgegnung auf die warmetheoretischen Betrachtungen des Hrn. E. Zermelo
228(1)
Rejoinder to the heat-theoretic considerations of Mr. E. Zermelo
229(17)
Zermelo 1896b
Introductory note: see under Zermelo 1896a Ueber mechanische Erklarungen irreversibler Vorgange. Eine Antwort auf Hrn. Boltzmann's "Entgegnung"
246(1)
On mechanical explanations of irreversible processes. An answer to Mr. Boltzmann's "rejoinder"
247(11)
Boltzmann 1897
Introductory note: see under Zermelo 1896a Zu Hrn. Zermelo's Abhandlung "Ueber die mechanische Erklarung irreversibler Vorgange"
258(1)
On Mr. Zermelo's paper "On the mechanical explanation of irreversible processes"
259(11)
Zermelo 1899a
Introductory note to 1899a
270(2)
Rudiger Thiele
Ueber die Bewegung eines Punktsystems bei Bedingungsungleichungen
272(1)
On the motion of a point system with constraint inequalities
273(7)
Zermelo s1899b
Introductory note to s1899b
280(2)
Rudiger Thiele
Wie bewegt sich ein unausdehnbarer materieller Faden unter dem Einfluss von Kraften mit dem Potentiale W(x, y, z)?
282(1)
How does an inextensible material string move under the action of forces with potential W(x, y, z)?
283(3)
Zermelo 1900
Introductory note to 1900
286(2)
Jos Uffink
Uber die Anwendung der Wahrscheinlichkeitsrechnung auf dynamische Systeme
288(1)
On the application of the calculus of probabilities to dynamical systems
289(11)
Zermelo 1902a
Introductory note to 1902a
300(16)
Alexey V. Borisov
Larisa A. Gazizullina
Sergei M. Ramodanov
Hydrodynamische Untersuchungen uber die Wirbelbewegungen in einer Kugelflache (Erste Mitteilung)
316(1)
Hydrodynamical investigations of vortex motions in the surface of a sphere (First communication)
317(75)
Zermelo s1902b
Introductory note: see under Zermelo 1902a Hydrodynamische Untersuchungen uber die Wirbelbewegungen in einer Kugelflache (Zweite Mitteilung)
392(1)
Hydrodynamical investigations of vortex motions in the surface of a sphere (Second communication)
393(71)
Zermelo s1902c
Introductory note: see under Zermelo 1902a
§5. Die absolute Bewegung
464(1)
§5. The absolute motion
465(19)
Zermelo 1902d
Introductory note to 1902d
484(4)
Rudiger Thiele
Zur Theorie der kurzesten Linien
488(1)
On the theory of shortest lines
489(5)
Zermelo 1904a
Introductory note to 1904a
494(2)
Rudiger Thiele
Uber die Herleitung der Differentialgleichung bei Variationsproblemen
496(1)
On the derivation of the differential equation in variational problems
497(15)
Hahn and Zermelo 1904
Introductory note to Hahn and Zermelo 1904
512(20)
Rudiger Thiele
Weiterentwicklung der Variationsrechnung in den letzten Jahren
532(1)
Further development of the calculus of variations in recent years
533(29)
Zermelo 1906
Introductory note to 1906
562(8)
Jos Uffink
Besprechung von Gibbs 1902 und Gibbs 1905
570(1)
Review of Gibbs 1902 and Gibbs 1905
571(23)
Riesenfeld and Zermelo 1909
Introductory note to Riesenfeld and Zermelo 1909
594(6)
Hans-Georg Bartel
Rainer Bruggemann
Die Einstellung der Grenzkonzentrationen an der Trennungsflache zweier Losungsmittel
600(1)
The settling of the boundary concentrations at the dividing surface of two solvents
601(15)
Zermelo 1928
Introductory note to 1928
616(6)
Mark E. Glickman
Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung
622(1)
The calculation of the results of a tournament as a maximum problem in the calculus of probabilities
623(49)
Zermelo 1930c
Introductory note to 1930c and 1931a
672(6)
Craig G. Eraser
Uber die Navigation in der Luft als Problem der Variationsrechnung
678(1)
On navigation in the air as a problem in the calculus of variations
679(9)
Zermelo 1931a
Introductory note: see under Zermelo 1930c
Uber das Navigationsproblem bei ruhender oder veranderlicher Windverteilung
688(1)
On the navigation problem for a calm or variable wind distribution
689(33)
Zermelo 1933a
Introductory note to 1933a
722(2)
Heinz-Dieter Ebbinghaus
Uber die Bruchlinien zentrierter Ovale. Wie zerbricht ein Stuck Zucker?
724(1)
On the lines of fracture of central ovals. How does a piece of sugar break up?
725(10)
Bibliography 735(38)
Index 773
H.-D. EBBINGHAUS: has worked in mathematical logic, mainly in model theory, during the last years also in the history of set theory. Author of the biography of Zermelo, "Zermelo - An Approach to His Life And Work", http://www.springer.com/978-3-540-49551-2.

AKIHIRO KANAMORI: works in set theory, the history of set theory, and has written several papers on Zermelo and set theory.