资源描述：
《Calculus of Variations by Gelfand and Fomin.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、CALCULUSOFVARIATIONSI.M.GELFANDS.V.FOMINMoscowStateUniversityRevisedEnglishEditionTranslatedandEditedbyRichardA.SilvermanPRENTICE-HALL,INC.EnglewoodCliffs,NewJerseySELECTEDRUSSIANPUBLICATIONSINTHEMATHEMATICALSCIENCESRichardA.Silverman,Editor©1963byPRENTICE-HALL,INC.EnglewoodCliffs,N.J.Allr
2、ightsreserved.Nopartofthisbookmaybereproducedinanyform,bymimeographoranyothermeans,withoutpermissioninwritingfromthepublisher.Currentprinting(lastdigit):201918171615PRENTICE-HALLINTERNATIONAL,INC.,LONDONPRENTICE-HALLOFAUSTRALIA,PTY.,LID.,SYDNEYPRENTICE-HALLOFCANADA,LID.,TORONTOPRENTICE-HAL
3、LOFINDIA(PRIVATE)LID.,NEWDELHIPRENTICE-HALLOFJAPAN.INC..TOKYOLibraryofCongressCatalogCardNumber63-18806PrintedintheUnitedStatesofAmericaC11229AUTHORS'PREFACEThepresentcourseisbasedonlecturesgivenbyI.M.GelfandintheMechanicsandMathematicsDepartmentofMoscowStateUniversity.However,thebookgoesc
4、onsiderablybeyondthematerialactuallypresentedinthelectures.Ouraimistogiveatreatmentoftheelementsofthecalculusofvariationsinaformwhichisbotheasilyunderstandableandsufficientlymodem.Considerableattentionisdevotedtophysicalapplicationsofvariationalmethods,e.g.,canonicalequations,variationalpr
5、inciplesofmechanicsandconservationlaws.Thereaderwhomerelywishestobecomefamiliarwiththemostbasicconceptsandmethodsofthecalculusofvariationsneedonlystudythefirstchapter.Thefirstthreechapters,takentogether,formamorecomprehensivecourseontheelementsofthecalculusofvariations,-butonewhichisstillq
6、uiteelementary(involvingonlynecessaryconditionsforextrema).Thefirstsixchapterscontain,moreorless,thematerialgivenintheusualuniversitycourseinthecalculusofvariations(withapplicationstothemechanicsofsystemswithafinitenumberofdegreesoffreedom),includingthetheoryoffields(presentedinasomewhatno
7、velway)andsufficientconditionsforweakandstrongextrema.Chapter7isdevotedtotheapplicationofvariationalmethodstothestudyofsystemswithinfinitelymanydegreesoffreedom.Chapter8containsabrieftreatmentofdirectmethodsinthecalculusofvariations.TheauthorsaregratefultoM.A.
