Moreprecisely,by(i),Imeanasystematicpresentationofthematerialgovernedbythedesireformathematicalperfectionandcompletenessoftheresults.Incontrastto(i),approach(ii)startsoutfromthequestion"Whatarethemostimportantapplications?"andthentriestoanswerthisquestionasquicklyaspossible.Here,onewalksdirectlyonthemainroadanddoesnotwanderintoalltheniceandinterestingsideroads.
Thepresentbookisbasedonthesecondapproach.Itisaddressedtoundergraduateandbeginninggraduatestudentsofmathematics,physics,andengineeringwhowanttolearnhowfunctionalanalysiselegantlysolvesmahematicalproblemsthatarerelatedtoourrealworldazldthathaveplayedanimportantroleinthehistoryofmathematics.Thereadershouldsensethatthetheoryisbeingdeveloped,notsimplyforitsownsake,butfortheeffectivesolutionofconcreteproblems.