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© 2000

Introduction to Calculus and Analysis II/1

Book

Part of the Classics in Mathematics book series (CLASSICS)

Table of contents

  1. Front Matter
    Pages N1-xxvii
  2. Richard Courant, Fritz John
    Pages 1-121
  3. Richard Courant, Fritz John
    Pages 122-217
  4. Richard Courant, Fritz John
    Pages 218-366
  5. Richard Courant, Fritz John
    Pages 367-542
  6. Back Matter
    Pages 543-557

About this book

Introduction

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)

Keywords

Derivative Differential equations Integral calculus Taylor's theorem calculus calculus of variations curves and surfaces differential equation extrema maximum mean value theorem measure minimum

Authors and affiliations

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

Bibliographic information

  • Book Title Introduction to Calculus and Analysis II/1
  • Authors Richard Courant
    Fritz John
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-57149-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-66569-4
  • eBook ISBN 978-3-642-57149-7
  • Series ISSN 1431-0821
  • Edition Number 1
  • Number of Pages XXV, 556
  • Number of Illustrations 157 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in 1974 by Interscience Publishers; a division of John Wiley and Sons, Inc.
  • Topics Analysis
  • Buy this book on publisher's site
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Reviews

From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991