Ernst Zermelo - Collected Works/Gesammelte Werke II: Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik

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Springer Science & Business Media, Aug 15, 2013 - Mathematics - 781 pages

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 Zermelo’s 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.

 

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Contents

Ernst Zermelos curriculum vitae
1
Introductory note to 1894
10
Untersuchungen zur VariationsRechnung
26
Investigations in the calculus of variations
27
Introductory note to 1896a 1896b and Boltzmann 1896 1897
188
Ueber einen Satz der Dynamik und die mechanische Wärmetheorie
214
On a theorem of dynamics and the mechanical heat theory
215
Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn E Zermelo
228
Introductory note to 1902d
484
Zur Theorie der kürzesten Linien
488
On the theory of shortest lines
489
Introductory note to 1904a
494
Über die Herleitung der Differentialgleichung bei Variationsproblemen
496
On the derivation of the differential equation in variational problems
497
Introductory note to Hahn and Zermelo 1904
512
Weiterentwicklung der Variationsrechnung in den letzten Jahren
532

Rejoinder to the heattheoretic considerations of Mr E Zermelo
229
Ueber mechanische Erklärungen irreversibler Vorgänge Eine Antwort auf Hrn Boltzmanns Entgegnung
246
On mechanical explanations of irreversible processes An answer to Mr Boltzmanns
247
Zu Hrn Zermelos Abhandlung Ueber die mechanische Erklärung irreversibler Vorgänge
258
On Mr Zermelos paper On the mechanical explanation of irreversible processes
259
Introductory note to 1899a
270
Ueber die Bewegung eines Punktsystemes bei Bedingungsungleichungen
272
On the motion of a point system with constraint inequalities
273
Introductory note to s1899b
280
Wie bewegt sich ein unausdehnbarer materieller Faden unter dem Einfluss von Kräften mit dem Potentiale Wxyz?
282
How does an inextensible material string move under the action of forces with potential Wxyz?
283
Introductory note to 1900
286
Über die Anwendung der Wahrscheinlichkeitsrechnung auf dynamische Systeme
288
On the application of the calculus of probabilities to dynamical systems
289
Introductory note to 1902a s1902b and s1902c
300
Hydrodynamische Untersuchungen über die Wirbelbewegungen in einer Kugelfläche Erste Mitteilung
316
Hydrodynamical investigations of vortex motions in the surface of a sphere First communication
317
Hydrodynamische Untersuchungen über die Wirbelbewegungen in einer Kugelfläche Zweite Mitteilung
392
Hydrodynamical investigations of vortex motions in the surface of a sphere Second communication
393
5 Die absolute Bewegung
464
5 The absolute motion
465
Further development of the calculus of variations in recent years
533
Introductory note to 1906
561
Besprechung von Gibbs 1902 und Gibbs 1905
569
Review of Gibbs 1902 and Gibbs 1905
571
Introductory note to Riesenfeld and Zermelo 1909
593
Die Einstellung der Grenzkonzentrationen an der Trennungsfläche zweier Lösungsmittel
599
The settling of the boundary concentrations at the dividing surface of two solvents
601
Introductory note to 1928 1929
616
Die Berechnung der TurnierErgebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung
622
The calculation of the results of a tournament as a maximum problem in the calculus of probabilities
623
Introductory note to 1930c and 1931a
672
Über die Navigation in der Luft als Problem der Variationsrechnung
678
On navigation in the air as a problem in the calculus of variations
679
Über das Navigationsproblem bei ruhenderoder veränderlicher Windverteilung
688
On the navigation problem for a calm or variable wind distribution
689
Introductory note to 1933a
722
Über die Bruchlinien zentrierter Ovale Wie zerbricht ein Stück Zucker?
724
On the lines of fracture of central ovals How does a piece of sugar break up?
725
Bibliography
734
Index
773
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About the author (2013)

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.

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