AP微积分课程设计Word文档格式.docx

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