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© 2002

Short Calculus

The Original Edition of “A First Course in Calculus”

Benefits

  • Covers all of the topics traditionally taught in the first-year claculus sequence in a brief and elementary fashion

Textbook
  • 39k Downloads

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Serge Lang
    Pages 1-13
  3. Serge Lang
    Pages 14-34
  4. Serge Lang
    Pages 35-64
  5. Serge Lang
    Pages 65-78
  6. Serge Lang
    Pages 79-93
  7. Serge Lang
    Pages 94-106
  8. Serge Lang
    Pages 107-115
  9. Serge Lang
    Pages 116-133
  10. Serge Lang
    Pages 134-152
  11. Serge Lang
    Pages 153-162
  12. Serge Lang
    Pages 163-177
  13. Serge Lang
    Pages 178-182
  14. Serge Lang
    Pages 183-194
  15. Serge Lang
    Pages 195-210
  16. Serge Lang
    Pages 211-226
  17. Back Matter
    Pages 227-263

About this book

Introduction

This is a reprint of "A First Course in Calculus," which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students'background was not as substantial as it might be. We are now back to those times, so it's time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950.

Keywords

calculus derivative differential equation exponential function logarithm maximum mean value theorem minimum

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title Short Calculus
  • Book Subtitle The Original Edition of “A First Course in Calculus”
  • Authors Serge Lang
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4613-0077-9
  • Copyright Information Springer-Verlag New York, Inc. 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-0-387-95327-4
  • eBook ISBN 978-1-4613-0077-9
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XII, 260
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
  • Buy this book on publisher's site

Reviews

From the reviews:

"...Lang's present book is a source of interesting ideas and brilliant techniques."
Acta Scientarium Mathematicarum

"... It is an admirable straightforward introduction to calculus."
Mathematika

"A First Course in Calculus went through five editions since the early sixties. Now the original edition of A First Course in Calculus is available again. The approach is the one that was successful decades ago, involving clarity and adjusted to a time when the students’ background was not as substantial as it might have been. … The audience is intended to consist of those taking the first calculus course, in high school or college." (G. Kirlinger, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003)

"This is a reprint of the original edition of Lang’s A first course in calculus, which was first published in 1964. … The treatment is ‘as rigorous as any mathematician would wish it’ … . There are quite a lot of exercises … they are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging. … There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." (Gerry Leversha, The Mathematical Gazette, Vol. 86 (507), 2002)