Format:
1 Online-Ressource (XXIX, 781 p)
ISBN:
9783540708568
Series Statement:
Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften 23
Content:
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
Note:
Description based upon print version of record
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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; Ernst Zermelo's curriculum vitae; Introductory note to 1894; 1. Sufficient conditions before Weierstrass; 2. Weierstrass; 3. Zermelo's dissertation; 4. Further discussion of Zermelo's theory; 5. Epilogue: Hilbert's invariant integral; Untersuchungen zur Variations-Rechnung; Über die Bedingungen, denen die Function unter dem Integralzeichen genügen muss.
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Investigations in the calculus of variationsOn the conditions to be met by the function under the integral sign.; Definition und erste notwendige Bedingungen des Minimums.; Definition and first necessary conditions of the minimum.; Einführung der Function E.; Introduction of the function E.; Aufstellung hinreichender Bedingungen.; Specification of sufficient conditions.; Thesen.; Vita.; Theses .; Vita.; Introductory note to 1896a, 1896b, and Boltzmann 1896, 1897; 1. The background to the Zermelo-Boltzmann controversy; 1.1. Theoretical physics in the late 19th century: Boltzmann and Planck
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1.2. Boltzmann and Planck's views1.3. The succession of Kirchhoff; 2. Boltzmann's work in the kinetic theory of gases; 3. The Zermelo-Boltzmann controversy; 3.1. Zermelo 1896a; 3.2. Boltzmann 1896; 3.3. Zermelo's response 1896b; 3.4. Boltzmann's second reply 1897; 3.5. Concluding remarks; Ueber einen Satz der Dynamik und die mechanische Wärmetheorie; On a theorem of dynamics and the mechanical heat theory; Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo; Rejoinder to the heat-theoretic considerations of Mr. E. Zermelo; Anhang.; Appendix.
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Ueber mechanische Erklärungen irreversibler Vorgänge. Eine Antwort auf Hrn. Boltzmann's „Entgegnung"On mechanical explanations of irreversible processes. An answer to Mr. Boltzmann's; Zu Hrn. Zermelo's Abhandlung „Ueber die mechanische Erklärung irreversibler Vorgänge"*; On Mr. Zermelo's paper "On the mechanical explanation of irreversible processes"*; Anhang.; Appendix.; Introductory note to 1899a; Ueber die Bewegung eines Punktsystemes bei Bedingungsungleichungen; On the motion of a point system with constraint inequalities; Introductory note to s1899b
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Wie bewegt sich ein unausdehnbarer materieller Faden unter dem Einfluss von Kräften mit dem Potentiale W(x,y,z)?*How does an inextensible material string move under the action of forces with potential W(x,y,z)?; Introductory note to 1900; Über die Anwendung der Wahrscheinlichkeitsrechnung auf dynamische Systeme*; On the application of the calculus of probabilities to dynamical systems*; Introductory note to 1902a, s1902b, and s1902c; Introduction; Chapters 1 and 2 (1902a); Hydrodynamics on arbitrary surfaces; Application of the theory to the sphere. Concept of point vortex; Stationary motions
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Chapters 3 and 4 (s1902b)
Additional Edition:
ISBN 9783540708551
Additional Edition:
Print version Ernst Zermelo - Collected Works/Gesammelte Werke II : Volume II/Band II - Calculus of Variations, Applied Mathematics, and Physics/Variationsrechnung, Angewandte Mathematik und Physik
Additional Edition:
Erscheint auch als Druck-Ausgabe Zermelo, Ernst, 1871 - 1953 Collected works ; 2: Calculus of variations, applied mathematics, and physics Berlin : Springer, 2013 ISBN 9783540708551
Language:
English
DOI:
10.1007/978-3-540-70856-8
URL:
Volltext
(lizenzpflichtig)
Author information:
Zermelo, Ernst 1871-1953
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