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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is wellillustrated, wellmotivated and very wellprovided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)
 About the authors

Biography of Richard Courant
Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence.
For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John.
(P.D. Lax)
Biography of Fritz John
Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was halfJewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994.
John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMOfunctions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty.
(J. Moser)  Reviews

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is wellillustrated, wellmotivated and very wellprovided with a multitude of unusually useful and accessible exercises. [...]It is the best text known to the reviewer for anyone trying to make an analysis course less abstract." The Mathematical Gazette
 Table of contents (9 chapters)


Introduction
Pages 1118

The Fundamental Ideas of the Integral and Differential Calculus
Pages 119200

The Techniques of Calculus
Pages 201323

Applications in Physics and Geometry
Pages 324439

Taylor’s Expansion
Pages 440480

Table of contents (9 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to Calculus and Analysis I
 Authors

 Richard Courant
 Fritz John
 Series Title
 Classics in Mathematics
 Copyright
 1999
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642586040
 DOI
 10.1007/9783642586040
 Softcover ISBN
 9783540650584
 Series ISSN
 14310821
 Edition Number
 1
 Number of Pages
 XXIII, 661
 Number of Illustrations
 184 b/w illustrations
 Additional Information
 Originally published by Interscience Publishers, Inc., 1965
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