A First Course in Analysis

This rigorous textbook is intended for a year-long analysis or advanced calculus course for
advanced undergraduate or beginning graduate students.Starting with detailed,slow-paced
proofs that allow students toacquirefacilityinreadingandwritingproofs,itclearlyand
conciselyexplainsthebasicsofdifferentiationandintegrationoffunctionsofoneandsev-
eralvariables,andcoversthetheoremsofGreen,Gauss,andStokes.Minimalprerequisites
areassumed,andrelevantlinearalgebratopicsarereviewedrightbeforetheyareneeded,
makingthematerialaccessibletostudentsfromdiversebackgrounds.Abstracttopicsare
preceded by concreteexamplestofacilitateunderstanding–e.g.beforeintroducingdiffer-
entialforms,thetextexamineslow-dimensionalexamples.Themeaningandimportanceof
resultsarethoroughlydiscussed,andnumerousexercisesofvaryingdifficultygivestudents
ampleopportunitytotestandimprovetheirknowledgeofthisdifficultyetvitalsubject.