Advanced Calculus

A Differential Forms Approach

  • Harold M. Edwards

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Harold M. Edwards
    Pages 1-21
  3. Harold M. Edwards
    Pages 22-51
  4. Harold M. Edwards
    Pages 52-75
  5. Harold M. Edwards
    Pages 76-131
  6. Harold M. Edwards
    Pages 132-195
  7. Harold M. Edwards
    Pages 196-225
  8. Harold M. Edwards
    Pages 226-264
  9. Harold M. Edwards
    Pages 265-356
  10. Harold M. Edwards
    Pages 357-455
  11. Back Matter
    Pages 456-508

About this book


​​​In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics.


This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view.


The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies.


The most important feature…is that it is fun—it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject.

—The American Mathematical Monthly (First Review)


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 rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical.

—The American Mathematical Monthly (1994) Based on the Second Edition



Lagrange multipliers Stokes' theorem differential calculus integrals linear algegra vector analysis

Authors and affiliations

  • Harold M. Edwards
    • 1
  1. 1.New York University, Courant InstituteNew YorkUSA

Bibliographic information

  • DOI
  • Copyright Information Harold M. Edwards 2014
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8411-2
  • Online ISBN 978-0-8176-8412-9
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • About this book