Richard Courant: Differential and Integral calculus English edition

In 1934 Richard Courant published an English edition of his German text Differential and Integral calculus. In a Preface to the English edition, Courant explains how the English edition came to be published. We give this below.

We also give the Preface to Courant's German edition at this link.

Differential and Integral calculus by Richard Courant

Preface to the English edition

When American colleagues urged me to publish an English edition of my lectures on the differential and integral calculus, I at first hesitated. I felt that owing to the difference between the methods of teaching the calculus in Germany and in Britain and America a simple translation was out of the question, and that fundamental changes would be required in order to meet the needs of English-speaking students.

My doubts were not laid to rest until I found a competent colleague in Professor E J McShane, of the University of Virginia, who was prepared not only to act as translator but also - after personal consultation with me - to make the improvements and alterations necessary for the English edition.

Apart from many matters of detail the principal changes are these: (1) the English edition contains a large number of classified examples; (2) the division of material between the two volumes differs somewhat from that in the German text. In addition to a detailed account of the theory of functions of one variable, the present volume contains (in Chapter X) a sketch of the differentiation and integration of functions of several variables. The second volume deals in full with functions of several independent variables, and includes the elements of vector analysis. There is also a more systematic discussion of differential equations, and an appendix on the foundations of the theory of real numbers.

Thus the first volume contains the material for a course in elementary calculus, while the subject-matter of the second volume is more advanced. In the first volume, however, there is much which should be omitted from a first course. These sections, intended for students wishing to penetrate more deeply into the theory, are collected in the appendices to the chapters, so that beginners can study the book without inconvenience, omitting or postponing the reading of these appendices.

R Courant
Cambridge, England
June 1934

JOC/EFR November 2006

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