These volumes are museum pieces. The origins of the first edition [Vol. I, Interscience, New York, 1965; Zbl 137, 29; Vol. II, 1974; Zbl 294:26003], here reproduced unchanged, go back to Courant's Vorlesungen über Differential- und Integralrechnung of 1927, which the authors claim to have been the first textbook to treat calculus as a unified subject. This claim reflects the European disregard of American mathematics that was common until around 1940: Osgood's Introduction to the calculus (1921) and Advanced calculus (1925) were just as unified, although somewhat less comprehensive. The authors' preface says that their volumes avoid ``the dogmatic style which conceals the motivation and the roots of the calculus in intuitive reality….It seems extremely important that students and instructors should be protected from smug purism.'' One can easily agree with the second objective, but readers somewhat younger than the reviewer may find the authors' attempts at motivation peculiar, since practically all the motivation is from classical physics. The two volumes go far enough to introduce calculus of variations, Fourier series, and complex analysis. In keeping with the preceding quotation, they maintain the level of sophistication that was standard in the 1920s. There is, of course, no modern terminology or notation, and also no recognition that some material could have been presented more simply than was traditional. At least one fallacious proof from Courant's book of 1927 has been retained.
Reviewer: Boas, R. P. [form MathSciNet]