© 1986

A First Course in Calculus


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

Table of contents

  1. Front Matter
    Pages N2-XV
  2. Review of Basic Material

    1. Front Matter
      Pages 1-1
    2. Serge Lang
      Pages 3-20
    3. Serge Lang
      Pages 21-54
  3. Differentiation and Elementary Functions

    1. Front Matter
      Pages 55-55
    2. Serge Lang
      Pages 57-116
    3. Serge Lang
      Pages 117-158
    4. Serge Lang
      Pages 159-180
    5. Serge Lang
      Pages 181-215
    6. Serge Lang
      Pages 216-235
    7. Serge Lang
      Pages 236-283
  4. Integration

    1. Front Matter
      Pages 285-285
    2. Serge Lang
      Pages 287-311
    3. Serge Lang
      Pages 312-334
    4. Serge Lang
      Pages 335-378
    5. Serge Lang
      Pages 379-423
  5. Taylor’s Formula and Series

    1. Front Matter
      Pages 425-425
    2. Serge Lang
      Pages 427-472
    3. Serge Lang
      Pages 473-500
  6. Functions of Several Variables

    1. Front Matter
      Pages 521-521

About this book


The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica­ tions which accompany them. The very talented students, with an ob­ vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. One writes an advanced monograph for oneself, because one wants to give permanent form to one's vision of some beautiful part of mathematics, not otherwise ac­ cessible, somewhat in the manner of a composer setting down his sym­ phony in musical notation. This book is written for the students to give them an immediate, and pleasant, access to the subject. I hope that I have struck a proper com­ promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject. In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course. Rigor. This does not mean that so-called rigor has to be abandoned.


calculus derivative differential equation logarithm mean value theorem

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title A First Course in Calculus
  • Authors Serge Lang
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-96201-6
  • Softcover ISBN 978-1-4612-6428-6
  • eBook ISBN 978-1-4419-8532-3
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 5
  • Number of Pages XV, 731
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Addison-Wesley Publishing Company, 1978, 1973, 1968, 1964
  • Topics Real Functions
  • Buy this book on publisher's site