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1、JerroldMarsdenandAlanWeinsteinAreaofrectangleA=lwcircleA=nr2triangleA=+bhSurfaceAreaofsphereA=47ir2cylinderA=2nrhVolumeofboxV=lwhsphereV=4nr3cylinderV=7ir2hconeV=4(areaofbase)x(height)TrigonometricIdentitiesPythagoreancos28+sin26'=I,1+tan28=sec28,cot2@+1=csc28Par
2、itysin(-8)=-sinO,cos(-8)=cos8,tan(-8)=-tan0CSC(-8)=-cscB,sec(-8)=sec8,cot(-%)=-cot8Co-relationscosO=sin(T--01,cscO=sec(T--81,cot8=tan(;--01Additionformulassin(@+4)=sin8cos++cos0sin+sin(8-+)=sin8cos+-cos0sin+cos(8++)=cos0cos+-sin8sin+cos(8-+)=cos8cos++sin8sin+(tan
3、0+tan+)tan(@++)=(1-tan8tan+)(tan8-tan+)tan(8-+)=(1+tan8tan+)Double-angleformulassin28=2sin8cos8cos28=cos28-sin28=2cos28-I=1-2sin282tan0tan28=(1-tan2@)Half-angleformulas.20-1-COSB1-~0~28sin---orsin2@=22228-1+caseorcos2@=1+cos28COS---222tan8sin8-1-cos8ortan8=1-cos2
4、8-=---------21fcos8sin0sin26'Productformulas1sin8sin+=-[cos(8-+)-cos(8++)I21cos8cos+=-[cos(8++)+cos(8-+)I2sin8cos+=1.[sin(@++)+sin(8-+)I2Copyright1985Springer-Verlag.Allrightsreserved.ToNancyandMargoCopyright1985Springer-Verlag.Allrightsreserved.JerroldMarsdenAla
5、nWeinsteinCaliforniaInstituteofTechnologyDepartmentofMathematicsControlandDynamicalSystems107-81UniversityofCaliforniaPasadena,California91125Berkeley,California94720USAUSAEditorialBoardS.AxlerF.W.GehringK.A.RibetMathematicsDepartmentMathematicsDepartmentDepartme
6、ntofSanFranciscoStateEastHallMathematicsUniversityUniversityofMichiganUniversityofCaliforniaSanFrancisco,CA94132AnnArbor,MI48109atBerkeleyUSAUSABerkeley,CA94720-3840USAMathematicsSubiectClassification(2000):26-01CoverphotographbyNancyWilliamsMarsden.LibraryofCong
7、ressCataloginginPublicationDataMarsden,JerroldE.Calculus11.(Undergraduatetextsinmathematics)Includesindex.1.Calculus.11.Weinstein,Alan.11.Marsden,JerroldE.Calculus.111.Title.IV.Title:Calculustwo.V.Series.QA303.M33721984b51584-5480PreviouseditionCalculusO1980byThe
8、Benjamin/CummingsPublishingCompany.O1985bySpringer-VeriagNewYorkInc.Allrightsresewed.Nopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissi
