微积分和数学分析引论（第1卷 英文版）

　　During 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 successful operation with infinite processes or limits. Two of these processes， differentiation and inte- gration， became the core of the systematic Differential and Integral Calculus， often simply called "Calculus，" basic for all of analysis.The importance of the new discoveries and methods was immediately felt and caused profound intellectual excitement. Yet， to gain mastery of the powerful art appeared at first a formidable task， for the avail-able publications were scanty， unsystematic， and often lacking in clarity. Thus， it was fortunate indeed for mathematics and science in general that leaders in the new movement soon recognized the vital need for writing textbooks aimed at making the subject ac-cessible to a public much larger than the very small intellectual elite of the early days. One of the greatest mathematicians of modern times，Leonard Euler， established in introductory books a firm tradition and these books of the eighteenth century have remained sources of inspira-tion until today， even though much progress has been made in the clarification and simplification of the material.After Euler， one author after the other adhered to the separation of differential calculus from integral calculus， thereby obscuring a keypoint， the reciprocity between differentiation and integration. Only in1927 when the first edition of R. Courant's German Vorlesungen iiber Differential und Integrairechnung， appeared in the Springer-Verlagwas this separation eliminated and the calculus presented as a unifiedsubject.

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