a quick introduction to tensor analysis - r. sharipov

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1、2MSC97U20PACS01.30.PpR.A.Sharipov.QuickIntroductiontoTensorAnalysis:lecturenotes.Freelydistributedon-line.Isfreeforindividualuseandeducationalpurposes.Anycommercialusewithoutwrittenconsentfromtheauthorisprohibited.ThisbookwaswrittenaslecturenotesforclassesthatItaughttounde

2、rgraduatestudentsmajoringinphysicsinFebruary2004duringmytimeasaguestinstructoratTheUniversityofAkron,whichwassupportedbyDr.SergeiF.Lyuksyutov'sgrantfromtheNationalResearchCouncilundertheCOBASEprogram.These4classeshavebeentaughtintheframeofaregularElectromagnetismcourseasan

3、introductiontotensorialmethods.Iwrotethisbookina"do-it-yourself"stylesothatIgiveonlyadraftoftensortheory,whichincludesformulatingdenitionsandtheoremsandgivingbasicideasandformulas.Allotherworksuchasprovingconsistenceofdenitions,derivingformulas,provingtheoremsorcompletin

4、gdetailstoproofsislefttothereaderintheformofnumerousexercises.Ihopethatthisstylemakeslearningthesubjectreallyquickandmoreeectiveforunderstandingandmemorizing.IamgratefultoDepartmentChairProf.RobertR.Mallikfortheopportunitytoteachclassesandthustobeinvolvedfullyintheatmosph

5、ereofanAmericanuniversity.IamalsogratefultoMr.M.Boiwka(mboiwka@hotmail.com)Mr.A.Calabrese(ajc10@uakron.edu)Mr.J.Comer(funnybef@lycos.com)Mr.A.Mozinski(arm5@uakron.edu)Mr.M.J.Shepard(sheppp2000@yahoo.com)forattendingmyclassesandreadingthemanuscriptofthisbook.Iwouldliketoesp

6、eciallyacknowledgeandthankMr.JeComerforcorrectingthegrammarandwordinginit.Contactstoauthor.Oce:MathematicsDepartment,BashkirStateUniversity,32Frunzestreet,450074Ufa,RussiaPhone:7-(3472)-23-67-18Fax:7-(3472)-23-67-74Home:5Rabochayastreet,450003Ufa,RussiaPhone:7-(917)-75-5

7、5-786E-mails:RSharipov@ic.bashedu.ru,r-sharipov@mail.ru,rasharipov@hotmail.com,URL:http://www.geocities.com/r-sharipovCopyRightcSharipovR.A.,2004CONTENTS.CONTENTS................................................................................................3.CHAPTERI.PREL

8、IMINARYINFORMATION...........................................4.x1.Geometricalandphysicalv