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Mathematics for Physics - gatech.edu

MathematicsforPhysicsA guidedtourforgraduatestudentsMichaelSton eandPaulGoldbartPIMANDER-CASAUBONA lexandria Florence LondoniiCopyrightc ,P. thismaterialcanbe reproduced,storedortransmittedwithoutthe writtenpermissionof informationcontact:MichaelStoneor PaulGoldbart,Department of Physics ,Universityof Illinoisat Urbana-Champaign,1110 WestGreenStreet,Urbana,Illinois61801-308 0, thememoryof Mike'smother,AileenStone:9 9 = Paul'smotherandfather, greatmany peoplehave encouragedus alongtheway:Ourteachersat theUniversity of Cambridge,theUniversity of California-LosAngeles, { yourquestionsandenthusiasmhave helped shape |faculty andsta |attheUniversity of Illinoisat Urbana-Champaign{ how fortunatewe areto have a community sorich in bothaccomplishment :KyreandSteve andGinna.}}

The second part (Chapters 10 to 14) focuses on modern di erential ge-ometry and topology, with an eye to its application to physics. The tools of calculus on manifolds, especially the exterior calculus, are introduced, and vii. viii PREFACE used to investigate classical mechanics, electromagnetism, and non-abelian

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