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© 1999

Introduction to Calculus and Analysis I

Benefits

  • It is the best known textbook to the reviewer for anyone trying to make an analysis course less abstract."

  • This book is highly recommended both to instructors and students."

Book

Part of the Classics in Mathematics book series (CLASSICS)

Table of contents

  1. Front Matter
    Pages N1-xxiii
  2. Richard Courant, Fritz John
    Pages 1-118
  3. Richard Courant, Fritz John
    Pages 119-200
  4. Richard Courant, Fritz John
    Pages 201-323
  5. Richard Courant, Fritz John
    Pages 324-439
  6. Richard Courant, Fritz John
    Pages 440-480
  7. Richard Courant, Fritz John
    Pages 481-509
  8. Richard Courant, Fritz John
    Pages 510-570
  9. Richard Courant, Fritz John
    Pages 571-632
  10. Richard Courant, Fritz John
    Pages 633-649
  11. Back Matter
    Pages 650-661

About this book

Introduction

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 There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry.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)

Keywords

Fourier series calculus differential equation numerical methods real analysis

Authors and affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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)

Bibliographic information

  • Book Title Introduction to Calculus and Analysis I
  • Authors Richard Courant
    Fritz John
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-58604-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-65058-4
  • eBook ISBN 978-3-642-58604-0
  • Series ISSN 1431-0821
  • Edition Number 1
  • Number of Pages XXIII, 661
  • Number of Illustrations 184 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Interscience Publishers, Inc., 1965
  • Topics Real Functions
    Special Functions
  • Buy this book on publisher's site

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