ThisclassictextbyadistinguishedmathematicianandformerProfessorofMathematicsatHarvardUniversity,leadsstudentsfamiliarwithelementarycalculusintoconfrontingandsolvingmoretheoreticalproblemsofadvancedcalculus.Inhisprefacetothefirstedition,ProfessorWidderalsorecommendsvariouswaysthebookmaybeusedasatextinbothappliedmathematicsandengineering.Believingthatclarityofexpositiondependslargelyonprecisionofstatement,theauthorhastakenpainstostateexactlywhatistobeprovedineverycase.Eachsectionconsistsofdefinitions,theorems,proofs,examplesandexercises.Anefforthasbeenmadetomakethestatementofeachtheoremsoconcisethatthestudentcanseeataglancetheessentialhypothesesandconclusions.Forthissecondedition,theauthorhasimprovedthetreatmentofStieltjesintegralstomakeitmoreusefultothereaderlessthanfamiliarwiththebasicfactsabouttheRiemannintegral.InadditionthematerialonserieshasbeenaugmentedbytheinclusionofthemethodofpartialsummationoftheSchwarz-Holderinequalities,andofadditionalresultsaboutpowerseries.Carefullyselectedexercises,gradedindifficulty,arefoundinabundancethroughoutthebook;answerstomanyofthemarecontainedinafinalsection.
