Classics in Mathematics

Introduction to Calculus and Analysis I

Authors: Courant, Richard, John, Fritz

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About this book

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided 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 There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry.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 half-Jewish 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 BMO-functions (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 well-illustrated, well-motivated and very well-provided 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

    Courant, Richard (et al.)

    Pages 1-118

  • The Fundamental Ideas of the Integral and Differential Calculus

    Courant, Richard (et al.)

    Pages 119-200

  • The Techniques of Calculus

    Courant, Richard (et al.)

    Pages 201-323

  • Applications in Physics and Geometry

    Courant, Richard (et al.)

    Pages 324-439

  • Taylor’s Expansion

    Courant, Richard (et al.)

    Pages 440-480

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-58604-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-540-65058-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Calculus and Analysis I
Authors
Series Title
Classics in Mathematics
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58604-0
DOI
10.1007/978-3-642-58604-0
Softcover ISBN
978-3-540-65058-4
Series ISSN
1431-0821
Edition Number
1
Number of Pages
XXIII, 661
Number of Illustrations and Tables
184 b/w illustrations
Additional Information
Originally published by Interscience Publishers, Inc., 1965
Topics