Calculus of Variations

BasedonaseriesoflecturesgivenbyI.M.GelfandatMoscowStateUniversity,thisbookactuallygoesconsiderablybeyondthematerialpresentedinthelectures.Theaimistogiveatreatmentoftheelementsofthecalculusofvariationsinaformbotheasilyunderstandableandsufficientlymodern.Considerableattentionisdevotedtophysicalapplicationsofvariationalmethods,e.g.,canonicalequations,variationalprinciplesofmechanics,andconservationlaws.Thereaderwhomerelywishestobecomefamiliarwiththemostbasicconceptsandmethodsofthecalculusofvariationsneedonlystudythefirstchapter.Studentswishingamoreextensivetreatment,however,willfindthefirstsixchapterscompriseacompleteuniversity-levelcourseinthesubject,includingthetheoryoffieldsandsufficientconditionsforweakandstrongextrema.Chapter7considerstheapplicationofvariationalmethodstothestudyofsystemswithinfinitedegreesoffreedom,andChapter8dealswithdirectmethodsinthecalculusofvariations.TheproblemsfollowingeachchapterweremadespeciallyforthisEnglish-languageedition,andmanyofthemcommentfurtheroncorrespondingpartsofthetext.Twoappendicesandsuggestionsforsupplementaryreadingroundoutthetext.Substantiallyrevisedandcorrectedbythetranslator,thisinexpensiveneweditionwillbewelcomedbyadvancedundergraduateandgraduatestudentsofmathematicsandphysics.