Calculus_BC_Syllabus_1[1] AP微积分教学大纲.pdf

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1、AP®CalculusBCSyllabus1Numbercrunchingandsymbolmanipulationareonlysmallpartsoflearningcal-culus.Iwantmystudentstofeeltheyunderstandeachconceptwestudy.Oneofthemajorgoalsisforthestudentstolearnhowtousepreciselanguagetodescribetheseconceptsandtherelationshipsbetwe

2、enideas.CoursePlanner[C2]C2—ThecourseteachesPrimaryTextbookalltopicsassociatedwithFunctions,Graphs,Finney,RossL.,FranklinDemana,BertWaits,andDanielKennedy.Calculus:andLimits;Derivatives;Graphical,Numerical,Algebraic.Reading,Mass.:Addison-Wesley,2007.Integrals;

3、andPolynomialApproximationsandSeriesasdelineatedThechapternumbersfollowthetextbook.NotethatweworkonChapter10beforeintheCalculusBCChapter9.TopicOutlineintheAPCalculusCourseDescription.Chapter1:PrerequisitesforCalculus(7days)•Elementaryfunctions:oLinear,power,ex

4、ponential/logarithmic,trigonometric/inversetrigonometric•Parametricequations•GettingfamiliarwiththegraphingcalculatorChapter2:LimitsandContinuity(10days)•Limits:oLimitatapoint,limitatinfinity,infinitelimitsoPropertiesoflimits•Continuity•Tangentlinetoacurve•Slo

5、peofacurveatapointChapter3:Derivatives(15days)•Definitionofƒ′•Derivativeatapoint•Relatingthegraphsofƒandƒ′•Whendoesƒ′(a)failtoexist?1•Rulesfordifferentiation:oSum,product,quotient•ChainRule•Implicitdifferentiation•Derivativesoftrigonometric,inversetrigonometri

6、c,exponentialandlogarithmicfunctionsChapter4:ApplicationsofDerivatives(17days)•MeanValueTheorem•Usingthederivativetofind:oCriticalpoint(s)andextremevaluesoWhenthefunctionisincreasingordecreasingoPoint(s)ofinflectionoWhenthefunctionisconcaveuporconcavedown•Opti

7、mizationproblems•Usingthetangentlinetoapproximatefunctionvalues•Newton’sMethod•Differentialsandchange•RelatedratesChapter5:TheDefiniteIntegral(14days)•RAM(RectangleApproximationMethod)•Riemannsums•Findinganantiderivative•Usingadefiniteintegraltofindarea,volume

8、,averagevalueofafunction•FundamentalTheoremofCalculus•Approximatingthedefiniteintegral:oTrapezoidalRule,Simpson’sRule,ErrorAnalysis2Chapter6:DifferentialEquationsandMathematicalMod