calculus II-3

1,Chapter11Vector-ValuedFunctions(向量值函数),InthisChapter,wewillknowsomeimportantconcepts.Vector-ValuedFunctionsTheCalculusofVector-ValuedFunctionsCurvature(曲率)TangentandNormalVectors,2,Example1:AirplaneFlightPath,VectorsIndicatingPosition,3,Section11.1Vector-ValuedFunctions,Vector-ValuedFunctions(向量值函数),4,Example2,5,Example3,6,Example4,7,Example5,8,Example6:Matching,9,ArcLengthin,10,ArcLengthFormula,11,Example7IntersectionofConeandPlane,12,Section11.2TheCalculusofVector-ValuedFunctions,TheLimits,13,TheContinuity,14,15,TheDifferentiation,16,17,TheTangentVectors,18,19,TheIntegration,20,21,Section11.4Curvature(曲率),22,23,SameorDifferent?,24,Notice:therateofchangeoftheunittangentvectorswithrespecttoarclengthalongthecurvewillgiveusameasureofsharpness.,25,TheCurvature(曲率),26,27,28,29,30,Section11.5TangentandNormalVectors(切向量与法向量),31,32,ThePrincipalUnitNormalVector(主要单位法向量),33,34,35,36,TheBinormalVectors(副法线向量),37,38,TheNormalPlaneandTheOsculatingPlane(法平面与密切平面),39,TheOsculatingCircle(密切圆),40,41,TangentialandNormalComponentsofAcceleration,42,43,Section11.6ParametricSurfaces(参数曲面),Motivation:Recallthecircularhelixgivenparametricallyby,44,45,Example1,46,Example2,Identifyandsketchthesurfacedefinedbyparametricequations,47,HyperbolicCosineandSineFunctions,Forparametricequationsofhyperboloidsandhyperbolicparaboloids,itisconvenienttousethehyperbolicfunctionscoshxandsinhxgivenby,48,Example3,Identifyandsketchthesurfacedefinedbyparametricequations,49,Example4,Findaparametricrepresentationofthehyperbolicparaboloid,50