This soft cover reprint of the original 1994 edition begins by with a lucid review of differential forms and proceeds to fundamental theorems of calculus and Stokes' theorem. Covers differential forms in linear algebra, and more. Includes numerous exercises.

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 featureis that it is funit 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

Affordable reprint of a classic textbook Presents advanced calculus using the theory of differential forms Makes modern mathematics accessible to students via physical intuition and applications Includes supplementary material: sn.pub/extras

Autorentext

Harold M. Edwards [1936-2020] was Professor Emeritus of Mathematics at New York University. His research interests lay in number theory, algebra, and the history and philosophy of mathematics. He authored numerous books, including Riemann's Zeta Function (1974, 2001) and Fermat's Last Theorem (1977), for which he received the Leroy P. Steele Prize for mathematical exposition in 1980. David A. Cox (Contributing Author) is Professor Emeritus of Mathematics in the Department of Mathematics and Statistics of Amherst College. He received the Leroy P. Steele Prize for mathematical exposition in 2016 for his book Ideals, Varieties, and Algorithms, with John Little and Donal O'Shea.

Inhalt
Constant Forms.- Integrals.- Integration and Differentiation.- Linear Algebra.- Differential Calculus.- Integral Calculus.- Practical Methods of Solution.- Applications.- Further Study of Limits.- Appendices.- Answers to Exercises.- Index.