Analysis in Euclidean Space

DevelopedforanintroductorycourseinmathematicalanalysisatMIT，thistextfocusesonconcepts，principles，andmethods.Itsintroductionstorealandcomplexanalysisarecloselyformulated，andtheyconstituteanaturalintroductiontocomplexfunctiontheory.
Startingwithanoverviewoftherealnumbersystem，thetextpresentsresultsforsubsetsandfunctionsrelatedtoEuclideanspaceofndimensions.Itoffersarigorousreviewofthefundamentalsofcalculus，emphasizingpowerseriesexpansionsandintroducingthetheoryofcomplex-analyticfunctions.Subsequentchapterscoversequencesoffunctions，normedlinearspaces，andtheLebesgueinterval.Theydiscussmostofthebasicpropertiesofintegralandmeasure，includingabrieflookatorthogonalexpansions.Achapterondifferentiablemappingsconcludesthetext，addressingimplicitandinversefunctiontheoremsandthechangeofvariabletheorem.Exercisesappearthroughoutthebook，andextensivesupplementarymaterialincludesabibliography，listofsymbols，index，andappendixwithbackgroundinelementarysettheory