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Birkhäuser

Advanced Calculus

A Differential Forms Approach

  • Textbook
  • © 1994

Overview

Authors:
  1. Harold M. Edwards

    1. Courant Institute, New York University, New York, USA

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
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  2. Constant Forms

    • Harold M. Edwards
    Pages 1-21

  3. Integrals

    • Harold M. Edwards
    Pages 22-51

  4. Integration and Differentiation

    • Harold M. Edwards
    Pages 52-75

  5. Linear Algebra

    • Harold M. Edwards
    Pages 76-131

  6. Differential Calculus

    • Harold M. Edwards
    Pages 132-195

  7. Integral Calculus

    • Harold M. Edwards
    Pages 196-225

  8. Practical Methods of Solution

    • Harold M. Edwards
    Pages 226-264

  9. Applications

    • Harold M. Edwards
    Pages 265-356

  10. Further Study of Limits

    • Harold M. Edwards
    Pages 357-455

  11. Back Matter

    Pages 456-508
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Keywords

About this book

My first book had a perilous childhood. With this new edition, I hope it has reached a secure middle age. The book was born in 1969 as an "innovative text­ book"-a breed everyone claims to want but which usu­ ally goes straight to the orphanage. My original plan had been to write a small supplementary textbook on differen­ tial forms, but overly optimistic publishers talked me out of this modest intention and into the wholly unrealistic ob­ jective (especially unrealistic for an unknown 30-year-old author) of writing a full-scale advanced calculus course that would revolutionize the way advanced calculus was taught and sell lots of books in the process. I have never regretted the effort that I expended in the pursuit of this hopeless dream-{}nly that the book was published as a textbook and marketed as a textbook, with the result that the case for differential forms that it tried to make was hardly heard. It received a favorable tele­ graphic review of a few lines in the American Mathematical Monthly, and that was it. The only other way a potential reader could learn of the book's existence was to read an advertisement or to encounter one of the publisher's sales­ men. Ironically, my subsequent books-Riemann :S Zeta Function, Fermat:S Last Theorem and Galois Theory-sold many more copies than the original edition of Advanced Calculus, even though they were written with no commer­ cial motive at all and were directed to a narrower group of readers.

Reviews

"This book can serve as a delightful guide to advanced calculus, giving firm foundations to further studies."

–Acta Sci. Math

"An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically and physically intuitive but mathematically rigorous, entertaining but serious. Remarkably diverse applications, physical and mathematical."

–The American Mathematical Monthly

Authors and Affiliations

  • Courant Institute, New York University, New York, USA

    Harold M. Edwards

Bibliographic Information

  • Book Title: Advanced Calculus

  • Book Subtitle: A Differential Forms Approach

  • Authors: Harold M. Edwards

  • DOI: https://doi.org/10.1007/978-1-4612-0271-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Harold M. Edwards 1994

  • eBook ISBN: 978-1-4612-0271-4Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: XV, 508

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Originally published by Houghton Mifflin Company

  • Topics: Analysis, Functional Analysis, Real Functions, Sequences, Series, Summability

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