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1、1234LightandMatterFullerton,Californiawww.lightandmatter.comcopyright2005BenjaminCrowellrev.April26,2008ThisbookislicensedundertheCreativeCom-monsAttribution-ShareAlikelicense,version1.0,http://creativecommons.org/licenses/by-sa/1.0/,exceptforthosephotographsanddrawingso
2、fwhichIamnottheauthor,aslistedinthephotocredits.Ifyouagreetothelicense,itgrantsyoucertainprivilegesthatyouwouldnototherwisehave,suchastherighttocopythebook,ordownloadthedigitalversionfreeofchargefromwww.lightandmatter.com.Atyouroption,youmayalsocopythisbookundertheGNUFre
3、eDocumentationLicenseversion1.2,http://www.gnu.org/licenses/fdl.txt,withnoinvariantsections,nofront-covertexts,andnoback-covertexts.51RatesofChange3.4Applications.....60Averages,60.
4、Work,61.
5、1.1Changeindiscretesteps9Probability,61.Twosidesofthesamecoin,Problems........67
6、9.
7、Someguesses,11.1.2Continuouschange..12Aderivative,14.
8、Properties4Techniquesofthederivative,15.
9、4.1Newton’smethod...69Higher-orderpolynomials,4.2Implicitdifferentiation.7016.
10、Thesecondderivative,4.3Taylorseries.....7116.
11、Maximaandminima,4.4Methodsofintegration.7618.Cha
12、ngeofvariable,76.
13、Problems........21Integrationbyparts,78.
14、Partialfractions,79.2Toinfinity—andProblems........83beyond!5Complexnumber2.1Infinitesimals.....232.2Safeuseofinfinitesimals26techniques2.3Theproductrule...305.1Reviewofcomplex2.4Thechainrule....33numbers........852
15、.5Exponentialsand5.2Euler’sformula....88logarithms.......345.3Partialfractionsrevisited90Theexponential,34.
16、TheProblems........91logarithm,36.2.6Quotients......376Improperintegrals2.7Differentiationonacomputer........386.1Integratingafunctionthat2.8Continuity......41blow
17、sup........932.9Limits.......426.2Limitsofintegrationatinfinity.........94L'H^opital'srule,45.
18、Anotherperspectiveoninde-Problems........96terminateforms,47.
19、Limitsatin nity,48.7IteratedintegralsProblems........507.1Integralsinsideintegrals977.2Applications.....993Integrat
20、ion7.3Polarcoordinates...1013.1Definiteandindefinite7.4Sphericalandcylindricalintegrals........55coordina
