Undergraduate Texts in Mathematics

Functions of Several Variables

Authors: Fleming, Wendell H

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eBook $59.99
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  • ISBN 978-1-4684-9461-7
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  • ISBN 978-0-387-90206-7
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About this Textbook

The purpose of this book is to give a systematic development of differential and integral calculus for functions of several variables. The traditional topics from advanced calculus are included: maxima and minima, chain rule, implicit function theorem, multiple integrals, divergence and Stokes's theorems, and so on. However, the treatment differs in several important respects from the traditional one. Vector notation is used throughout, and the distinction is maintained between n-dimensional euclidean space En and its dual. The elements of the Lebesgue theory of integrals are given. In place of the traditional vector analysis in £3, we introduce exterior algebra and the calculus of exterior differential forms. The formulas of vector analysis then become special cases of formulas about differential forms and integrals over manifolds lying in P. The book is suitable for a one-year course at the advanced undergraduate level. By omitting certain chapters, a one semester course can be based on it. For instance, if the students already have a good knowledge of partial differentiation and the elementary topology of P, then substantial parts of Chapters 4, 5, 7, and 8 can be covered in a semester. Some knowledge of linear algebra is presumed. However, results from linear algebra are reviewed as needed (in some cases without proof). A number of changes have been made in the first edition. Many of these were suggested by classroom experience. A new Chapter 2 on elementary topology has been added.

Table of contents (8 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4684-9461-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-90206-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4684-9463-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Functions of Several Variables
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1977
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-9461-7
DOI
10.1007/978-1-4684-9461-7
Hardcover ISBN
978-0-387-90206-7
Softcover ISBN
978-1-4684-9463-1
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XII, 412
Additional Information
Originally published by Addison/Wesley
Topics