AP微积分5分制胜

图书标准信息

• 作者 [美]马（William Ma）、[美]惠特（Carolyn Wheater） 著
• 出版社 西安交通大学出版社
• 出版时间 2013-06
• 版次 1
• ISBN 9787560552484
• 定价 78.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 508页
• 字数 382千字

【内容简介】

　　《AP微积分5分制胜》引进自美国知名教育出版公司McGraw-HillEducation，由AP考试相关领域专家编写，是美国本土大学课堂使用教材，可以帮助考生提前适应全英学习模式。此系列中，AP各学科分册紧扣考试命题特点，以“五步”方案为学习框架，囊括与考试相关的学科要点。同时，还精选针对性练习以及全真模拟试题，配以准确答案和详尽解析，利于考生巩固所学，紧抓重点，取得高分。

【作者简介】

　　William Ma，教授微积分多年；曾获得哥伦比亚大学学士和硕士学位；后又曾担任何瑞克斯学区的数学部主席，直至退休。

　　Carolyn Wheater，毕业于马萨诸塞大学和玛丽蒙特曼哈顿大学，教授数学近30年；现在南丁格尔班福德学校担任初高中部数学老师。

【目录】

STEP1SetUpYourStudyPlan
1WhatYouNeedtoKnowAbouttheAPCalculusAB/BCExams
1.1WhatIsCoveredontheAPCalculusExams?
1.2WhatIstheFormatoftheAPCalculusAP/BCExams?
1.3WhatAretheAdvancedPlacementExamGrades?
HowIstheAPCalculusExamGradeCalculated?
1.4WhichGraphingCalculatorsAreAllowedfortheExam?
CalculatorsandOtherDevicesNotAllowedfortheAPCalculusExam
OtherRestrictionsonCalculators
2HowtoPlanYourTime
2.1ThreeApproachestoPreparingfortheAPCalculusExam
OverviewoftheThreePlans
2.2CalendarforEachPlan
SummaryoftheThreeStudyPlans

STEP2DetermineYourTestReadiness
3TakeaDiagnosticExam
3.1GettingStarted!
3.2DiagnosticTest
3.3AnswerstoDiagnosticTest
3.4SolutionstoDiagnosticTest
3.5CalculateYourScore
Short-AnswerQuestions
APCalculusAB/BCDiagnosticExam

STEP3DevelopStrategiesforSuccess
4HowtoApproachEachQuestionType
4.1TheMultiple-ChoiceQuestions
4.2TheFree-ResponseQuestions
4.3UsingaGraphingCalculator
4.4TakingtheExam
WhatDoINeedtoBringtotheExam?
TipsforTakingtheExam

STEP4ReviewtheKnowledgeYouNeedtoScoreHigh
5LimitsandContinuity
5.1TheLimitofaFunction
DefinitionandPropertiesofLimits
EvaluatingLimits
One-SidedLimits
SqueezeTheorem
5.2LimitsInvolvingInfinities
InfiniteLimits(asx→a)
LimitsatInfinity(asx→±∞)
HorizontalandVerticalAsymptotes
5.3ContinuityofaFunction
ContinuityofaFunctionataNumber
ContinuityofaFunctionoveranInterval
TheoremsonContinuity
5.4RapidReview
5.5PracticeProblems
5.6CumulativeReviewProblems
5.7SolutionstoPracticeProblems
5.8SolutionstoCumulativeReviewProblems
6Differentiation
6.1DerivativesofAlgebraicFunctions
DefinitionoftheDerivativeofaFunction
PowerRule
TheSum,Difference,Product,andQuotientRules
TheChainRule
6.2DerivativesofTrigonometric,InverseTrigonometric,
Exponential,andLogarithmicFunctions
DerivativesofTrigonometricFunctions
DerivativesofInverseTrigonometricFunctions
DerivativesofExponentialandLogarithmicFunctions
6.3ImplicitDifferentiation
ProcedureforImplicitDifferentiation
6.4ApproximatingaDerivative
6.5DerivativesofInverseFunctions
6.6HigherOrderDerivatives
6.7IndeterminateForms
L'Hopital'sRuleforIndeterminateForms
6.8RapidReview
6.9PracticeProblems
6.10CumulativeReviewProblems
6.11SolutionstoPracticeProblems
6.12SolutionstoCumulativeReviewProblems
7GraphsofFunctionsandDerivatives
7.1Rolle'sTheorem,MeanValueTheorem,andExtremeValueTheorem
Rolle'sTheorem
MeanValueTheorem
ExtremeValueTheorem
7.2DeterminingtheBehaviorofFunctions
TestforIncreasingandDecreasingFunctions
FirstDerivativeTestandSecondDerivativeTestforRelativeExtrema
TestforConcavityandPointsofInflection
7.3SketchingtheGraphsofFunctions
GraphingwithoutCalculators
GraphingwithCalculators
7.4GraphsofDerivatives
7.5Parametric,Polar,andVectorRepresentations
ParametricCurves
PolarEquations
TypesofPolarGraphs
SymmetryofPolarGraphs
Vectors
VectorArithmetic
7.6RapidReview
7.7PracticeProblems
7.8CumulativeReviewProblems
7.9SolutionstoPracticeProblems
7.10SolutionstoCumulativeReviewProblems
8ApplicationsofDerivatives
8.1RelatedRate
GeneralProcedureforSolvingRelatedRateProblems
CommonRelatedRateProblems
InvertedCone(WaterTank)Problem
ShadowProblem
AngleofElevationProblem
8.2AppliedMaximumandMinimumProblems
GeneralProcedureforSolvingAppliedMaximumandMinimumProblems
DistanceProblem
AreaandVolumeProblem
BusinessProblems
8.3RapidReview
8.4PracticeProblems
8.5CumulativeReviewProblems
8.6SolutionstoPracticeProblems
8.7SolutionstoCumulativeReviewProblems
9MoreApplicationsofDerivatives
9.1TangentandNormalLines
TangentLines
NormalLines
9.2LinearApproximations
TangentLineApproximation(orLinearApproximation)
EstimatingthenthRootofaNumber
EstimatingtheValueofaTrigonometricFunctionofanAngle
9.3MotionAlongaLine
InstantaneousVelocityandAcceleration
VerticalMotion
HorizontalMotion
9.4Parametric,Polar,andVectorDerivatives
DerivativesofParametricEquations
Position,Speed,andAcceleration
DerivativesofPolarEquations
VelocityandAccelerationofVectorFunctions
9.5RapidReview
9.6PracticeProblems
9.7CumulativeReviewProblems
9.8SolutionstoPracticeProblems
9.9SolutionstoCumulativeReviewProblems
10Integration
10.1EvaluatingBasicIntegrals
AntiderivativesandIntegrationFormulas
EvaluatingIntegrals
10.2IntegrationbyU-Substitution
TheU-SubstitutionMethod
U-SubstitutionandAlgebraicFunctions
U-SubstitutionandTrigonometricFunctions
U-SubstitutionandInverseTrigonometricFunctions
U-SubstitutionandLogarithmicandExponentialFunctions
10.3TechniquesofIntegration
IntegrationbyParts
IntegrationbyPartialFractions
10.4RapidReview
10.5PracticeProblems
10.6CumulativeReviewProblems
10.7SolutionstoPracticeProblems
10.8SolutionstoCumulativeReviewProblems
11DefiniteIntegrals
11.1RiemannSumsandDefiniteIntegrals
SigmaNotationorSummationNotation
DefinitionofaRiemannSum
DefinitionofaDefiniteIntegral
PropertiesofDefiniteIntegrals
11.2FundamentalTheoremsofCalculus
FirstFundamentalTheoremofCalculus
SecondFundamentalTheoremofCalculus
11.3EvaluatingDefiniteIntegrals
DefiniteIntegralsInvolvingAlgebraicFunctions
DefiniteIntegralsInvolvingAbsoluteValue
DefiniteIntegralsInvolvingTrigonometric,Logarithmic,andExponentialFunctions
DefiniteIntegralsInvolvingOddandEvenFunctions
11.4ImproperIntegrals
InfiniteIntervalsofIntegration
InfiniteDiscontinuities
11.5RapidReview
11.6PracticeProblems
11.7CumulativeReviewProblems
11.8SolutionstoPracticeProblems
11.9SolutionstoCumulativeReviewProblems
12AreasandVolumes
12.1TheFunctionF(x)= f(t)dt
12.2ApproximatingtheAreaUnderaCurve
RectangularApproximations
TrapezoidalApproximations
AreaUnderaCurve
AreaBetweenTwoCurves
12.4VolumesandDefiniteIntegrals
SolidswithKnownCrossSections
TheDiscMethod
TheWasherMethod
12.5IntegrationofParametric,Polar,andVectorCurves
Area,ArcLength,andSurfaceAreaforParametricCurves
AreaandArcLengthforPolarCurves
IntegrationofaVector-ValuedFunction
MeanValueTheoremforIntegrals
12.6RapidReview
12.7PracticeProblems
12.8CumulativeReviewProblems
12.9SolutionstoPracticeProblems
12.10SolutionstoCumulativeReviewProblems
13MoreApplicationsofDefiniteIntegrals
13.1AverageValueofaFunction
AverageValueofaFunctionon[a,b]
13.2DistanceTraveledProblems
13.3DefiniteIntegralasAccumulatedChange
BusinessProblems
TemperatureProblem
LeakageProblems
GrowthProblem
13.4DifferentialEquations
ExponentialGrowth/DecayProblems
SeparableDifferentialEquations
13.5SlopeFields
13.6LogisticDifferentialEquations
13.7Euler'sMethod
ApproximatingSolutionsofDifferentialEquationsbyEuler'sMethod
13.8RapidReview
13.9PracticeProblems
13.10CumulativeReviewProblems
13.11SolutionstoPracticeProblems
13.12SolutionstoCumulativeReviewProblems
14Series(ForCalculusBCStudentsOnly)
14.1SequencesandSeries
Convergence
14.2TypesofSeries
p-Series
HarmonicSeries
GeometricSeries
DecimalExpansion
14.3ConvergenceTests
IntegralTest
RatioTest
ComparisonTest
LimitComparisonTest
BibliographyandWebSites
FormulasandTheorems
14.4AlternatingSeries
ErrorBound
AbsoluteConvergence
14.5PowerSeries
RadiusandIntervalofConvergence
14.6TaylorSeries
TaylorSeriesandMacLaurinSeries
CommonMacLaurinSeries
14.7OperationsonSeries
Substitution
DifferentiationandIntegration
ErrorBounds
14.8RapidReview
14.9PracticeProblems
14.10CumulativeReviewProblems
14.11SolutionstoPracticeProblems
14.12SolutionstoCumulativeReviewProblems

STEP5BuildYourTest-TakingConfidence
APCalculusABPracticeExam
APCalculusABPracticeExam
APCalculusBCPracticeExam
APCalculusBCPracticeExam
Appendixes
FormulasandTheorems
BibliographyandWebSites
……