　　本书是为国际文凭课程大学预科项目（IBDP）设计的数学微积分选修辅导书，内容涵盖了IBDP数学HL微积分教学大纲的所有内容。全书分为6个模块，每个模块以知识点分节，每节包含知识点梳理、例题演示和相关习题这3部分，每个模块后有综合题练习。书中的例题和习题都力求提供详细的解题步骤或多种思考方向。本书重点在于微积分科目系统的解题训练，以及专业的IB答题思路指导。

作者简介

　　作者於嵩是上海世外中学的数学组组长。作者吴斌就职于上海世外教育集团，在教学之余还活跃于IB教育资源建设和IB教学推广。两位作者都是有十年左右教学经验的IB数学教师，同时也都是IB数学的考官，有丰富的IBDP数学教学经验和思考，具有非常专业的水平，同时在IB数学教育规划和课程体系建设方面都有专业的见解。

精彩书评

1.知识点清晰，非常适合IBDP学生。
2.非常好的书籍！因为市面上IB的教辅书很少，这本编辑整理得很好！
3.很管用！当复习资料再好不过了。
4.超级好！惊艳！纸质很舒服，例题和练习题都很好。
5.对我而言，非常难得的一本好书。
6.简直是iblearner的福音。

1Limits，continuousand
differentiablefunctions11.1Limitsofsequences1
1.2Limitsoffunctions3
1.3SqueezeTheorem9
1.4Continuityoffunctions11
1.5Differentiablefunctions16
Moduleonemiscellaneousquestions18
2Rolle�餾theoremand
MeanValueTheorem222.1Rolle�餾theorem22
2.2MeanValueTheorem(MVT)24
Moduletwomiscellaneousquestions29
3FundamentalTheoremof
Calculusandimproper
integrals343.1FundamentalTheoremofCalculus34
3.2Improperintegrationsoftheform
∫∞af(x)dx35
3.3Approximationofimproperintegrals38
Modulethreemiscellaneousquestions42
4Infiniteseriesand
powerseries454.1Sumofinfinitegeometricseries45
4.2TestforDivergence47
4.3IntegralTest48
4.4ComparisonTest51
4.5LimitComparisonTest54
4.6AlternatingSeriesTest56
4.7Absoluteandconditionalconvergence59
4.8RatioTest61
4.9Telescopingseries62
4.10Powerseries64
Modulefourmiscellaneousquestions67
5TaylorandMaclaurin
series705.1Revision:powerseriesandits
convergence70
5.2TaylorandMaclaurinseries76
5.3TaylorandMaclaurinpolynomials82
5.4TaylorandMaclaurinserieswith
their“friends”88
Modulefivemiscellaneousquestions99
6Differentialequation1096.1Introductiontodifferentialequation109
6.2Solvingthefirstorderdifferential
equationsbygraphicalmethod1116.3Solvingthefirstorderdifferential
equationsbynumericalmethod121
6.4Solvingthefirstorderdifferential
equationsbyanalyticmethod124
6.5Thefirstorderdifferentialequationand
theTaylororMaclaurinseries149
Modulesixmiscellaneousquestions156
Answersofexercises165

前言/序言

　　Whatisthemeaningof“IBISEE”?“IB”meanstheInternationalBaccalaureate.“I”meansthereader.“SEE”meansSummary，ExamplesandExercises.Itisthegeneralformatofeachmoduleinthisbook.
　　ThisbookiswrittenonlyforstudentswhochoosecalculusasoptioninhigherlevelmathematicsintheInternationalBaccalaureate（IB）DiplomaProgramme（DP）.Optiontopiccalculusiscoveredinthisbook.Andwedivideditintoseveralmodulesarrangedintheorderoftheauthors�餾ummarystrategy.
　　ThematerialscontainedinthisbookaredesignedtocomplementyourtextbookandIBSyllabus.ThisbookcontainstypesofquestionsmostfrequentlytestedinIBfinalexams.TheaimofthisbookistohelpIBstudentsandteachersprepareforthefinalexamination.
　　Thisbookconsistsof6modules.Foreachmodule，therearetheorysectionsandmanyworkedexamples.Thereaderswhofollowthesetwopartsshouldthenbeabletomakeconsiderableprogressthroughtheexercisesprovided.WestronglyrecommendthereaderstotakeIBpastyearexaminationsthatareprovidedbyIBtotestthemselvesafterfinishingreadingthisbook.
　　Attheendofeachmodule，thereareseveralquestionstohelpyoureviewtherulesandskillscoveredinthepreviousmodules.Forthesequestions，calculatorisallowedforeachquestion.Tableofsymbolsandnotations

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