Ernst Zermelo - Collected Works/Gesammelte Werke II, 2nd Edition

  • Published By:
  • ISBN-10: 3540708561
  • ISBN-13: 9783540708568
  • DDC: 510
  • Grade Level Range: College Freshman - College Senior
  • 781 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Other Frontmatter.
Half Title Page.
Other Frontmatter.
Other Frontmatter.
Other Frontmatter.
Title Page.
Copyright Page.
Preface to the Zermelo Edition.
Preface to Volume II.
Editorial Information.
Copyright Permissions.
Editors and Contributors of Introductory Notes.
Contents of volume II.
Contents of volume I.
Corrections to Volume I.
Other Frontmatter.
1: Ernst Zermelo's Curriculum Vitae.
2: Introductory Note to 1894.
3: Untersuchungen zur Variations-Rechnung.
4: Investigations in the Calculus of Variations.
5: Investigations in the Calculus of Variations.
6: Introductory note to 1896a, 1896b, and Boltzmann 1896, 1897.
7: Ueber Einen Satz der Dynamik Und Die Mechanische Wärmetheorie.
8: On a Theorem of Dynamics and the Mechanical Heat Theory.
9: Entgegnung Auf Die Wärmetheoretischen Betrachtungen des Hrn. E. Zermelo.
10: Rejoinder to the Heat-Theoretic Considerations of Mr. E. Zermelo.
11: Ueber Mechanische Erklärungen Irreversibler Vorgänge. Eine Antwort Auf Hrn. Boltzmann's “Entgegnung”.
12: On Mechanical Explanations of Irreversible Processes. An Answer to Mr. Boltzmann's “Rejoinder”.
13: Zu Hrn. Zermelo's Abhandlung “Ueber Die Mechanische Erklärung Irreversibler Vorgänge”*.
14: On Mr. Zermelo's Paper “On the Mechanical Explanation of Irreversible Processes”*.
15: Introductory Note to 1899a.
16: Ueber Die Bewegung Eines Punktsystemes Bei Bedingungsungleichungen.
17: On the Motion of a Point System with Constraint Inequalities.
18: Introductory Note to s1899b.
19: Wie Bewegt Sich Ein Unausdehnbarer Materieller Faden Unter Dem Einfluss Von Kräften Mit Dem Potentiale W(x, y, z)?.
20: How Does an Inextensible Material String Move under the Action of Forces with Potential W(x,y,z)?.
21: Introductory Note to 1900.
22: ÜBer Die Anwendung Der Wahrscheinlichkeitsrechnung Auf Dynamische Systeme*.
23: On the Application of the Calculus of Probabilities to Dynamical Systems*.
24: Introductory Note to 1902a, s1902b, and s1902c.
25: Hydrodynamische Untersuchungen über Die Wirbelbewegungen in Einer Kugelfläche (Erste Mitteilung) 1902a.
26: Hydrodynamical Investigations of Vortex Motions in the Surface of a Sphere (First communication).
27: Hydrodynamische Untersuchungen über die Wirbelbewegungen in einer Kugelfläche(Zweite Mitteilung).
28: Hydrodynamical Investigations of Vortex Motions in the Surface of a Sphere (Second communication).
29: §5. Die absolute Bewegung.
30: §5. The absolute motion*.
31: Introductory Note to 1902d.
32: Zur Theorie Der Kürzesten Linien.
33: On the theory of Shortest Lines.
34: Introductory Note to 1904a.
35: ÜBer Die Herleitung Der Differentialgleichung Bei Variationsproblemen.
36: On the Derivation of the Differential Equation in Variational Problems.
37: Introductory Note to Hahn and Zermelo 1904.
38: Weiterentwicklung Der Variationsrechnung in Den Letzten Jahren.
39: Further Development of the Calculus of Variations in Recent Years.
40: Introductory Note to 1906.
41: Besprechung Von Gibbs 1902 Und Gibbs 1905.
42: Review of Gibbs 1902 and Gibbs 1905.
43: Introductory Note to Riesenfeld and Zermelo 1909.
44: Die Einstellung Der Grenzkonzentrationen An Der Trennungsfläche Zweier Lösungsmittel.
45: The Settling of the Boundary Concentrations at the Dividing Surface of Two Solvents.
46: Introductory Note to 1928 (= 1929)*.
47: Die Berechnung Der Turnier-Ergebnisse Als Ein Maximumproblem Der Wahrscheinlichkeitsrechnung.
48: The Calculation of the Results of a Tournament as a Maximum Problem in the Calculus of Probabilities.
49: Introductory Note to 1930c and 1931a.
50: üBer Die Navigation in Der Luft Als Problem Der Variationsrechnung.
51: On Navigation in the Air as a Problem in the Calculus of Variations.
52: Über Das Navigationsproblem Bei Ruhender Oder Veränderlicher Windverteilung.
53: On the Navigation Problem for a Calm or Variable Wind Distribution.
54: Introductory Note to 1933a.
55: Über Die Bruchlinien Zentrierter Ovale. Wie Zerbricht Ein Stück Zucker?.
56: On the Lines of Fracture of Central Ovals. How does a Piece of Sugar Break up?.