AP微积分课程设计Word文档格式.docx
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AP微积分课程设计Word文档格式.docx
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课时分配
高一
第一学期
第一模块
集合(4课时)
函数与基本初等函数(32课时)
解析几何(9课时)
复合函数、反函数以及作图计算器的使用
高中课程:
6课时/周,共54课时;
AP微积分:
2课时/周,共18课时;
第二模块
直线与圆的方程(9课时)
圆锥曲线(8课时)
三角函数(16课时)
极限
极限的运算法则
第二学期
第三模块
三角恒等变换
反三角函数
导数
导数的基本公式
第四模块
立体几何
导数的运算法则
高
二
第
一
学
期
第五模块
常用逻辑用语
平面向量
解三角形
导数的应用
第六模块
数列
不等式
积分方程
微分方程
第七模块
复数
统计
计数原理
AP微积分总复习
AP微积分AB考试
第八模块
参数方程
极坐标
AP微积分BC
4课时/周,共36课时;
AP微积分BC:
高三
总
复习
总复习
毕业会考
微积分
其它大学预修课程
AP微积分BC考试
四、课程内容
Chapter2LimitsandDerivatives
第二章极限和导数
TeachingContent
教学内容
TeachingRequirementsandObjectives
教学要求和目标
Time
学时
TheTangentandVelocityProblems
切线和速率问题
Thestudentwillapplythederivativetosolveproblems,includingtangentandnormallinestoacurve,curvesketching,velocity,acceleration.
TheLimitofaFunction
函数的极限
Thestudentwilldefineandapplythepropertiesoflimitsoffunctions.
Thiswillincludelimitsofaconstant,sum,product,quotient,one-sidedlimits,limitsatinfinity,infinitelimits,andnonexistentlimits.
CalculatingLimitsUsingtheLimitLaws
利用极限法则计算极限
Continuity
连续性
Thestudentwillstatethedefinitionofcontinuityanddeterminewhereafunctioniscontinuousordiscontinuous.
Thiswillincludecontinuityatapoint;
continuityoveraclosedinterval;
andgraphicalinterpretationofcontinuityanddiscontinuity.
LimitsatInfinity;
HorizontalAsymptotes
无穷远处极限和水平渐近线
Thestudentwilldefineandapplythepropertiesofelementaryfunctions,includingalgebraic,trigonometric,exponential,andcompositefunctionsandtheirinverses,andgraphthesefunctionsusingagraphingcalculator.
Propertiesoffunctionswillincludedomains,ranges,combinations,odd,even,periodicity,
symmetry,asymptotes,zeros,upperand
lowerbounds,andintervalswherethefunctionis
increasingordecreasing.
Thestudentwillalsodefineandapplythe
propertiesoflimitsoffunctions.
Thiswillincludelimitsofaconstant,sum,
product,quotient,one-sidedlimits,limitsat
infinity,infinitelimits,andnonexistentlimits.
Tangents,Velocities,andOtherRatesofChange
切线、速度和其它的变化率
Derivatives
Thestudentwillfindthederivativeofanalgebraicfunctionbyusingthedefinitionofaderivative.
Thiswillincludeinvestigatinganddescribingtherelationshipbetweendifferentiabilityandcontinuity.
TheDerivativeasaFunction
导函数
Review
Chapter3DifferentiationRules
第三章导数法则
DerivativesofPolynomialsandExponentialFunctions
多项式函数和指数函数的导数
Thestudentwillapplyformulastofindthederivativeofalgebraic,trigonometric,exponential,andlogarithmicfunctionsandtheirinverses.
TheProductandQuotientRules
导数的乘法和除法运算法则
Thestudentwillapplyformulastofindthederivativeofthesumofelementaryfunctions.
RatesofChangeintheNaturalandSocialSciences
自然科学和社会科学中的变化率
Studentswillbeabletounderstandthemathematicalmodelingprocessofderivatives(ratesofchanges)intherealworld
ofTrigonometricFunctions
三角函数的导数
Studentswillbeabletousethedifferentiationrulesoftrigonometricfunctions
TheChainRule
链式法则
Thestudentwillapplyformulastofindthederivativeofthesum,product,quotient,inverseandcomposite(chainrule)ofelementaryfunctions.
Implicit
Differentiation
隐函数求导
Thestudentwillfindthederivativeofanimplicitlydefinedfunction.
Higher
高阶导数
Thestudentwillfindthehigherorderderivativesofalgebraic,trigonometric,exponential,andlogarithmicfunctions.
ofLogarithmicFunctions
对数函数的导数
Thestudentwilluselogarithmicdifferentiationasatechniquetodifferentiatenon-logarithmicfunctions.
HyperbolicFunctions
双曲函数
Thestudentwillbeabletounderstandthedefinitionofhyperbolicfunctions,andsolveforitsderivatives.
LinearApproximationsandDifferentials
线性逼近和微分
Thestudentwillapplythederivativetosolveproblems,includingtangentandnormallinestoacurve,curvesketching,velocity,acceleration,relatedratesofchange,Newton'
smethod,differentialsandlinearapproximations,andoptimizationproblems.
Chapter4ApplicationsofDifferentiation
第四章导数的应用
MaximumandMinimumValues
极大值和极小值
Thestudentwillbeabletounderstandextremevaluesofafunction,findcriticalvaluesofafunctionandfindextremevaluesofafunction.
TheMeanValueTheorem
中值定理
Thestudentwillstate(withoutproof)theMeanValueTheoremforderivativesandapplyitbothalgebraicallyandgraphically.
HowDerivativeAffecttheShapeofaGraph
导数是如何改变图像的形状
Thestudentwillgraphthesefunctionsusingagraphingcalculator,includingunderstandingandusingtheFirstDerivativeTestandtheSecondDerivativeTesttodeterminemin’sandmax’s.
IndeterminateFormsandL’Hospital’sRules
不定式和洛必达法则
Thestudentwillusel'
Hopital'
sruletofindthelimitoffunctionswhoselimitsyieldtheindeterminateforms:
0/0andinfinity/infinity
OptimizationProblems
最优化问题
Thestudentwillbeabletousederivativestosolveoptimizationproblems
Newton’sMethod
牛顿法则
ThestudentwillbeabletouseNewton’smethodtoapproximaterootsofanequation.
原函数(反导数)
Thestudentwillbeabletounderstandtheconceptofanantiderivative,thegeometryoftheantiderivativeandthatofslopefieldsandalsoworkrectilinearmotionproblemswithantiderivatives
Chapter5Integrals
第五章积分
AreasandDistances
面积和距离
Thestudentwillidentifythepropertiesofthedefiniteintegral.
ThiswillincludetheFundamentalTheoremofCalculusandthedefiniteintegralasanareaandasalimitofasumaswellasthefundamentaltheorem.
TheDefiniteIntegral
不定积分
Thestudentwillcomputeanapproximatevalueforadefiniteintegral.
ThiswillincludenumericalcalculationsusingRiemannSumsandtheTrapezoidalRule.
TheFundamentalTheoremofCalculus
微积分基本定理
ThiswillincludetheFundamentalTheoremofCalculusandthedefiniteintegralasanareaandasalimitofasumaswellasthefundamentaltheorem.Theintegralfromatoxoff(t)d(t)dt/dx=f(x)
IndefiniteIntegralsandtheNetChangeTheorem
不定积分和原函数定理
Thestudentwillfindtheindefiniteintegralofalgebraic,exponential,logarithmic,andtrigonometricfunctions.
TheSubstitutionRule
换元积分法
Thespecialintegrationtechniquesofsubstitution(changeofvariables)andintegrationbypartswillbeincluded.
Chapter6ApplicationsofIntegration
第六章积分的应用
AreasBetweenCurves
曲边面积
Thestudentwillapplythedefiniteintegraltosolveproblems.
Theseproblemswillincludefindingdistancetraveledonalineandvelocityfromaccelerationwithinitialconditions,growthanddecayproblems,solutionsofseparabledifferentialequations,theaveragevalueofafunction,areabetweencurves,volumesofsolidsofrevolutionabouttheaxesorlinesparalleltotheaxesusingdisc/washerandshellmethods,andvolumesofsolidswithknowncross-sectionalareas.
Volumes
体积
Theseproblemswillincludeareabetweencurves,volumesofsolidsofrevolutionabouttheaxesorlinesparalleltotheaxesusingdisc/washerandshellmethods,andvolumesofsolidswithknowncross-sectionalareas.
VolumesbyCylindricalShells
圆柱体体积
Theseproblemswillinclude…areabetweencurves,volumesofsolidsofrevolutionabouttheaxesorlinesparalleltotheaxesusingdisc/washerandshellmethods,andvolumesofsolidswithknowncross-sectionalareas.
Work
物体功
Theseproblemswillincludefindingdistancetraveledonalineandvelocityfromaccelerationwithinitialconditions,growthanddecayproblems,workdone.
AverageValueofaFunction
实函数均值
Theseproblemswillincludetheaveragevalueofafunction.
DensityFunction
密度函数
Thestudentwillappl
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