1、Classics in MathematicsRichard Courant,Fritz JohnIntroduction toCalculus andAnalysis I微积分和数学分析引论第1卷界圈士出版公司Springerwww.WPrefaceDuring the latter part of the seventeenth century the new mathe-matical analysis emerged as the dominating force in mathematics.It is characterized by the amazingly successfu
2、l operation with infiniteprocesses or limits.Two of these processes,differentiation and inte-gration,became the core of the systematic Differential and IntegralCalculus,often simply called Calculus,basic for all of analysis.The importance of the new discoveries and methods was immediatelyfelt and ca
3、used profound intellectual excitement.Yet,to gain masteryof the powerful art appeared at first a formidable task,for the avail-able publications were scanty,unsystematic,and often lacking inclarity.Thus,it was fortunate indeed for mathematics and sciencein general that leaders in the new movement so
4、on recognized thevital need for writing textbooks aimed at making the subject ac-cessible to a public much larger than the very small intellectual elite ofthe early days.One of the greatest mathematicians of modern times,Leonard Euler,established in introductory books a firm tradition andthese books
5、 of the eighteenth century have remained sources of inspira-tion until today,even though much progress has been made in theclarification and simplification of the material.After Euler,one author after the other adhered to the separation ofdifferential calculus from integral calculus,thereby obscurin
6、g a keypoint,the reciprocity between differentiation and integration.Only in1927 when the first edition of R.Courants German Vorlesungen uberDifferential und Integralrechnung,appeared in the Springer-Verlagwas this separation eliminated and the calculus presented as a unifiedsubject.From that German book and its subsequent editions the presentwork originated.With the cooperation of James and Virginia McShauea greatly expanded and modified English edition of the Calculus wesprepared and published by Blackie and Sons in Glasgow since 1934,and
