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1、ElementsofMathematicsforEconomicsandFinanceVassilisC.MavronandTimothyN.PhillipsElementsofMathematicsforEconomicsandFinanceWith77FiguresVassilisC.Mavron,MA,MSc,PhDTimothyN.Phillips,MA,MSc,DPhil,InstituteofMathematicalandPhysicalDScSciencesCardiffSchoolofMathema
2、ticsUniversityofWalesAberystwythCardiffUniversityAberystwythSY233BZSenghennyddRoadWales,UKCardiffCF244AGWales,UKMathematicsSubjectClassification(2000):91-01;91B02BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibr
3、aryLibraryofCongressControlNumber:2006928729ISBN-10:1-84628-560-7e-ISBN1-84628-561-5Printedonacid-freepaperISBN-13:978-1-84628-560-8©Springer-VerlagLondonLimited2007Apartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismorreview,aspermittedun
4、dertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced,storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublishers,orinthecaseofreprographicreproductioninaccordancewiththetermsoflicencesissuedbytheCopyrightLice
5、nsingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesenttothepublishers.Theuseofregisterednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantlawsandregulationsandtherefor
6、efreeforgeneraluse.Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyoftheinformationcontainedinthisbookandcannotacceptanylegalresponsibilityorliabilityforanyerrorsoromissionsthatmaybemade.PrintedintheUnitedStatesofAmerica(HAM)987654321
7、SpringerScience+BusinessMedia,LLCspringer.comPrefaceThemathematicscontainedinthisbookforstudentsofeconomicsandfinancehas,formanyyears,beengivenbytheauthorsintwosingle-semestercoursesattheUniversityofWalesAberystwyth.Theseweremathematicscoursesinaneconomicssetti
8、ng,givenbymathematiciansbasedintheDepartmentofMathematicsforstudentsintheFacultyofSocialSciencesorSchoolofMan-agement.Thechoiceofsubjectmatterandarrangementofmaterialreflectthiscoll
