P�ginas:770G�neros:12:PBKA:Calculus12:PBKJ:Differentialcalculus&equations12:PBKF:Functionalanalysis&transformsSinopsis: ,Part1beginswithanoverviewofpropertiesoftherealnumbersandstartstointroducethenotionsofsettheory.Theabsolutevalueandinparticularinequalitiesareconsideredingreatdetailbeforefunctionsandtheirbasicpropertiesarehandled.Fromthistheauthorsmovetodifferentialandintegralcalculus.Manyexamplesarediscussed.Proofsnotdependingonadeeperunderstandingofthecompletenessoftherealnumbersareprovided.Asatypicalcalculusmodule,thispartisthoughtasaninterfacefromschooltouniversityanalysis.Part2returnstothestructureoftherealnumbers,mostofalltotheproblemoftheircompletenesswhichisdiscussedingreatdepth.OncethecompletenessofthereallineissettledtheauthorsrevisitthemainresultsofPart1andprovidecompleteproofs.Moreovertheydevelopdifferentialandintegralcalculusonarigorousbasismuchfurtherbydiscussinguniformconvergenceandtheinterchangingoflimits,infiniteseries(includingTaylorseries)andinfiniteproducts,improperintegralsandthegammafunction.Inadditiontheydiscussedinmoredetailasusualmonotoneandconvexfunctions.Finally,theauthorssupplyanumberofAppendices,amongthemAppendicesonbasicmathematicallogic,moreonsettheory,thePeanoaxiomsandmathematicalinduction,andonfurtherdiscussionsofthecompletenessoftherealnumbers.Remarkably,VolumeIcontainsca.360problemswithcomplete,detailedsolutions._,

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This is a very good book for anyone interested in learning analysis. I highly recommend this book to anyone teaching or studying analysis at an undergraduate level. --Zentralblatt MATH

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The writing style is generally quite clear, and students should have little difficulty reading this book. The full seven-volume collection will no doubt be an indispensable reference for analysts and non-analysts alike, and this volume is an excellent start. --Mathematical Gazette

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