Synopsis
Ce traité moderne pionnier sur le calcul des variations étudie l'évolution du sujet d'Euler à Hilbert. Le texte aborde les problèmes de base avec suffisamment de généralité et de rigueur pour offrir une introduction solide à une étude sérieuse. Il fournit des définitions claires des concepts fondamentaux, des formulations précises des problèmes et des démonstrations rigoureuses de leurs solutions. De nombreux exemples sont résolus complètement, et des références systématiques sont données pour chaque théorème dès sa première apparition.
Les premiers chapitres abordent la première et la deuxième variation de l'intégrale, et les chapitres suivants couvrent les conditions suffisantes pour un extremum de l'intégrale et la théorie du problème de Weierstrass en représentation des paramètres; l'extension de Kneser de la théorie de Weierstrass pour couvrir le cas des points d'extrémité variables; et la théorie de Weierstrass des problèmes isopérimétriques. Le dernier chapitre présente une preuve approfondie du théorème d'existence de Hilbert.
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Lectures on the Calculus of Variations
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Dover Publications, 2018
ISBN 10 : 0486822362
ISBN 13 : 9780486822365
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Lectures on the Calculus of Variations (Paperback)
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ISBN 10 : 0486822362
ISBN 13 : 9780486822365
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Paperback. Etat : new. Paperback. This pioneering modern treatise on the calculus of variations studies the evolution of the subject from Euler to Hilbert. The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem. AUTHOR: Oskar Bolza (18571942) studied mathematics at the University of Berlin and later at Strasbourg. He taught at Johns Hopkins, Clark University, and the University of Chicago, returning to Germany 22 years later but retaining the University of Chicago title of Non-resident Professor of Mathematics for the rest of his life. He taught mathematics at the University of Freiburg until his 1933 retirement. Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9780486822365
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Lectures on the Calculus of Variations (Paperback)
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Dover Publications Inc., New York, 2018
ISBN 10 : 0486822362
ISBN 13 : 9780486822365
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Paperback. Etat : new. Paperback. This pioneering modern treatise on the calculus of variations studies the evolution of the subject from Euler to Hilbert. The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem. AUTHOR: Oskar Bolza (18571942) studied mathematics at the University of Berlin and later at Strasbourg. He taught at Johns Hopkins, Clark University, and the University of Chicago, returning to Germany 22 years later but retaining the University of Chicago title of Non-resident Professor of Mathematics for the rest of his life. He taught mathematics at the University of Freiburg until his 1933 retirement. Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de réf. du vendeur 9780486822365
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Lectures on the Calculus of Variations (Paperback)
Edité par
Dover Publications Inc., New York, 2018
ISBN 10 : 0486822362
ISBN 13 : 9780486822365
Neuf
Paperback
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Paperback. Etat : new. Paperback. This pioneering modern treatise on the calculus of variations studies the evolution of the subject from Euler to Hilbert. The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem. AUTHOR: Oskar Bolza (18571942) studied mathematics at the University of Berlin and later at Strasbourg. He taught at Johns Hopkins, Clark University, and the University of Chicago, returning to Germany 22 years later but retaining the University of Chicago title of Non-resident Professor of Mathematics for the rest of his life. He taught mathematics at the University of Freiburg until his 1933 retirement. Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9780486822365
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