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MathematicsforPhysicsA guidedtourforgraduatestudentsMichaelSton eandPaulGoldbartPIMANDER-CASAUBONAlexand ria Florence LondoniiCopyrightc ,P. thismaterialcanbe reproduced,storedortransmittedwithoutthe writtenpermissionof informationcontact:MichaelStoneor PaulGoldbart,Department of Physics ,Universityof Illinoisat Urbana-Champaign,1110WestGreenStreet,Urb ana,Illinois61801-3080, 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;andJenny, OllieandGreta{ we hope to be moreattentive now thatthisbookis CambridgeUniversity Press{ of Energy, whohave supportedourresearch over is basedona two-semestersequenceof coursestaught to incominggraduatestudents at theUniversity of Illinoisat Urbana-Champaign,pri-marilyphysicsstuden ts butalsosomefromotherbranchesof introducestudents to someof themathematicalmethods andconceptsthattheywill ndusefulin havesought to enliven thematerialby thereforeprovideillustrative theseillustrationsareclassicalbutmany aresmallpartsofcontemporaryresearch thetextandat theendof each chapterweprovidea collectionof}}}}

whole functions y(x) and returns a single number. Such objects are called functionals to distinguish them from ordinary functions. An ordinary func-tion is a map f: R !R. A functional J is a map J: C1(R) !R where C1(R) is the space of smooth (having derivatives of …

  Mathematics, Physics, Functions, Mathematics for physics