Introduction to Calculus and Analysis Volume I / Edition 1

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Overview

From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text.

"..this book intends to lead students directly to the heart of calculus & prepare them for active application of their knowledge, revealing the interconnections & purposes of the whole."

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Editorial Reviews

From the Publisher

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

Booknews
Reprint of the 1965 textbook (John Wiley and Sons) originally written by Courant in 1927 and translated into English in 1934. This first volume is concerned primarily with functions of a single variable. Problems and examples. No bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9783540650584
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/22/1998
  • Series: Classics in Mathematics Series
  • Edition description: Reprint of the 1st ed. Berlin, Heidelberg, New York 1989
  • Edition number: 1
  • Pages: 661
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.45 (d)

Meet the Author

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)

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Table of Contents

1 Introduction.- 2 The Fundamental Ideas of the Integral and Differential Calculus.- 3 The Techniques of Calculus.- 4 Applications in Physics and Geometry.- 5 Taylor’s Expansion.- 6 Numerical Methods.- 7 Infinite Sums and Products.- 8 Trigonometric Series.- 9 Differential Equations for the Simplest Types of Vibration.- List of Biographical Dates.
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Customer Reviews

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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted July 31, 2004

    a superb book for intelligent readers

    This book is a rewrite of the classic work by courant, As such it loses a bit of the old world charm of courant's work, but gains from a greater degree of clarity and precision. I especially recommend this work to honors calculus students. The focus is on explaining exactly why the results are true, and in this regard it has few peers.

    2 out of 2 people found this review helpful.

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