Geometrical Methods in Variational Problems by N.A. BobylovGeometrical Methods in Variational Problems by N.A. Bobylov

Geometrical Methods in Variational Problems

byN.A. Bobylov, S.V. Emel'yanov, S. Korovin

Paperback | October 13, 2012

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Since the building of all the Universe is perfect and is cre­ ated by the wisdom Creator, nothing arises in the Universe in which one cannot see the sense of some maXImum or mInImUm Euler God moves the Universe along geometrical lines Plato Mathematical models of most closed physical systems are based on vari­ ational principles, i.e., it is postulated that equations describing the evolu­ tion of a system are the Euler<_lagrange20_equations20_of20_a20_certain20_functional.20_in20_this20_connection2c_20_variational20_methods20_are20_one20_of20_the20_basic20_tools20_for20_studying20_many20_problems20_of20_natural20_sciences.20_the20_first20_problems20_related20_to20_the20_search20_for20_extrema20_appeared20_as20_far20_back20_as20_in20_ancient20_mathematics.20_they20_go20_back20_to20_archimedes2c_20_appolonius2c_20_and20_euclid.20_in20_many20_respects2c_20_the20_problems20_of20_seeking20_maxima20_and20_minima20_have20_stimulated20_the20_creation20_of20_differential20_calculus3b_20_the20_variational20_princ2ad_20_ciples20_of20_optics20_and20_mechanics2c_20_which20_were20_discovered20_in20_the20_seventeenth20_and20_eighteenth20_centuries2c_20_gave20_impetus20_to20_an20_intensive20_development20_of20_the20_calculus20_of20_variations.20_in20_one20_way20_or20_another2c_20_variational20_problems20_were20_of20_interest20_to20_such20_giants20_of20_natural20_sciences20_as20_fermat2c_20_newton2c_20_descartes2c_20_euler2c_20_huygens2c_20_1.20_bernoulli2c_20_j.20_bernoulli2c_20_legendre2c_20_jacobi2c_20_kepler2c_20_lac2ad_20_grange2c_20_and20_weierstrass. equations="" of="" a="" certain="" functional.="" in="" this="" _connection2c_="" variational="" methods="" are="" one="" the="" basic="" tools="" for="" studying="" many="" problems="" natural="" sciences.="" first="" related="" to="" search="" extrema="" appeared="" as="" far="" back="" ancient="" mathematics.="" they="" go="" _archimedes2c_="" _appolonius2c_="" and="" euclid.="" _respects2c_="" seeking="" maxima="" minima="" have="" stimulated="" creation="" differential="" _calculus3b_="" _princ2ad_="" ciples="" optics="" _mechanics2c_="" which="" were="" discovered="" seventeenth="" eighteenth="" _centuries2c_="" gave="" impetus="" an="" intensive="" development="" calculus="" variations.="" way="" or="" _another2c_="" interest="" such="" giants="" sciences="" _fermat2c_="" _newton2c_="" _descartes2c_="" _euler2c_="" _huygens2c_="" 1.="" _bernoulli2c_="" j.="" _legendre2c_="" _jacobi2c_="" _kepler2c_="" _lac2ad_="" _grange2c_="">
Title:Geometrical Methods in Variational ProblemsFormat:PaperbackDimensions:543 pages, 24 × 16 × 0.01 inPublished:October 13, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401059551

ISBN - 13:9789401059558

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Table of Contents

Preface. 1. Preliminaries. 2. Minimization of Nonlinear Functionals. 3. Homotopic Methods in Variational Problems. 4. Topological Characteristics of Extremals of Variational Problems. 5. Applications. Bibliographical Comments. References. Index.