© 1987

Calculus of Several Variables


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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Basic Material

    1. Front Matter
      Pages 1-1
    2. Serge Lang
      Pages 3-48
    3. Serge Lang
      Pages 49-65
    4. Serge Lang
      Pages 66-86
    5. Serge Lang
      Pages 87-120
  3. Maxima, Minima, and Taylor’s Formula

    1. Front Matter
      Pages 121-121
    2. Serge Lang
      Pages 123-142
    3. Serge Lang
      Pages 143-179
  4. Curve Integrals and Double Integrals

    1. Front Matter
      Pages 181-181
    2. Serge Lang
      Pages 183-205
    3. Serge Lang
      Pages 206-232
    4. Serge Lang
      Pages 233-268
    5. Serge Lang
      Pages 269-290
  5. Triple and Surface Integrals

    1. Front Matter
      Pages 291-291
    2. Serge Lang
      Pages 293-317
    3. Serge Lang
      Pages 318-364
  6. Mappings, Inverse Mappings, and Change of Variables Formula

    1. Front Matter
      Pages 365-365
    2. Serge Lang
      Pages 367-384
    3. Serge Lang
      Pages 385-411

About this book


The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.


Fourier series calculus derivative differential equation maximum minimum

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title Calculus of Several Variables
  • Authors Serge Lang
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York Inc. 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-96405-8
  • Softcover ISBN 978-1-4612-7001-0
  • eBook ISBN 978-1-4612-1068-9
  • Series ISSN 0172-6056
  • Edition Number 3
  • Number of Pages XII, 619
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Addison-Wesley, Reading, 1979
  • Topics Real Functions
  • Buy this book on publisher's site