calculus of finite differences - jordan

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1、CALCULUSOFFINITEDIFFERENCESBYINTRODUCTIONBYSECONDEDITIONCHELSEAPUBLISHINGCOMPANYNEWYORK,N.Y.1950i/4:PHINTEDINTHEIlNlTEDSTATESOFAMEHItXINTRODUCTIONThereismorethanmerecoincidenceinthefactthattherecentrapidgrowthinthetheoryandapplicationofmathema-ticalstatisticshasbeenaccomp

2、aniedbyarevivalininterestintheCalculusofFiniteDifferences.Thereasonforthispheno-menaisclear:thestudentofmathematicalstatisticsmustnowregardthefinitecalculusasjustasimportantatoolandpre-requisiteastheinfinitesimalcalculus.Tomymind,theprogressthathasbeenmadetodateinthedevel

3、opmentofthefinitecalculushasbeenmarkedandstimulatedbytheappearenceoffouroutstandingtexts.ThefirstofthesewasthetreatisebyGeorgeBoolethatappearedin1860.Idonotme&bythistounderestimatethevaluablecontributionsofearlierwritersonthissubjectortooverlooktheelaborateworkofLacroix.’

4、ImerelywishtostatethatBoolewasthefirsttopresent’thissubjectinaformbestsuitedtotheneedsofstudentandteacher.ThesecondmilestonewastheremarkableworkofNarlundthatappearedin1924.Thisbookpresentedthefirstrigoroustreatmentofthesubject,andwaswrittenfromthepointofviewofthemathemati

5、cianrather.thanthestatistician.Itwasmostoportune.’Steffensen’sInterpolation,thethirdofthefourtextstowhich‘Ihavereferred,presentsanexcellenttreatmentofonesectionoftheCalculusofFiniteDifferences,namelyinterpola-tionandsummationformulae,andmeritsthecommendationofbothmathemat

6、iciansandstatisticians.Idonothesitatetopredictthatthefourthofthetextsthat1Volume3ofTrait6duCalculDiffdrentieletduCalculInt&pl,entitledTrait6desdiffbencesetdesshies.S.F,Lacroix,1819.viIhaveinmind,ProfessorJordan’sCalculusofFiniteDifferen-ces,isdestinedtoremaintheclassictre

7、atmentofthissubject-especiallyforstatisticians-formanyyearstocome.Althoughaninspectionofthetableofcontentsrevealsacoveragesoextensivethattheworkofmorethan600pagesmightleadoneatfirsttoregardthisbookasanencyclopediaonthesubject,yetareadingofanychapterofthetextwillimpressthe

8、readerasafriendlylecturerevealinganununsualappreciationofbothrigorandthecomputingtechniquesoim-p