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...Lecture notes on vector and tensor algebra analysis ilya l shapiro departamento de f sica instituto ci encias exatas universidade federal juiz fora cep mg brazil preface theselecturenotesaretheresultofteachingahalf semester courseoftensorsforundergraduates in the department of physics at university same lectures were also given summer school institute mathematics brasilia where i was kindly invited by dra maria em lia guimara es dr guy grebot furthermore have used rst version these to teach students scientic initiation usually case independent study good learn material one since some original didactic elements we decided publish them are designed for second third year undergraduate student supposed help learning such disciplines course as classical mechanics electrodynamics special general relativity my purposes e g make derivation grad div rot curvilinear coordinates understandable this seems be useful or engineering those which going career theoretical may should continue their educa...