© 1977

Functions of Several Variables


Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Wendell Fleming
    Pages 1-27
  3. Wendell Fleming
    Pages 28-75
  4. Wendell Fleming
    Pages 76-118
  5. Wendell Fleming
    Pages 119-166
  6. Wendell Fleming
    Pages 167-244
  7. Wendell Fleming
    Pages 245-274
  8. Wendell Fleming
    Pages 275-320
  9. Wendell Fleming
    Pages 321-382
  10. Back Matter
    Pages 383-411

About this book


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.


Algebra Differentialform Differentialrechnung Functions Integralrechnung Manifold Topology Variable calculus function geometry theorem

Authors and affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • Book Title Functions of Several Variables
  • Authors Wendell Fleming
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 1977
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90206-7
  • Softcover ISBN 978-1-4684-9463-1
  • eBook ISBN 978-1-4684-9461-7
  • Series ISSN 0172-6056
  • Edition Number 2
  • Number of Pages XII, 412
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Addison/Wesley
  • Topics Calculus of Variations and Optimal Control; Optimization
  • Buy this book on publisher's site