A First Course in Mathematical Analysis[数学分析入门教程]

MathematicalAnalysis(oftencalledAdvancedCalculus)isgenerallyfoundbystudentstobeoneoftheirhardestcoursesinMathematics.Thistextusestheso-calledsequentialapproachtocontinuity,differentiabilityandintegrationtomakeiteasiertounderstandthesubject.TopicsthataregenerallyglossedoverinthestandardCalculuscoursesaregivencarefulstudyhere.Forexample,whatexactlyisa'continuous'function?Andhowexactlycanonegiveacarefuldefinitionof'integral'?ThelatterquestionisoftenoneofthemysteriouspointsinaCalculuscourse-anditisquitedifficulttogivearigoroustreatmentofintegration!Thetexthasalargenumberofdiagramsandhelpfulmarginnotes;andusesmanygradedexamplesandexercises,oftenwithcompletesolutions,toguidestudentsthroughthetrickypoints.Itissuitableforself-studyoruseinparallelwithastandarduniversitycourseonthesubject.