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A First Course in Calculus

  • Textbook
  • © 1986

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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

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Table of contents (18 chapters)

  1. Front Matter

    Pages N2-XV
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  2. Review of Basic Material

    1. Front Matter

      Pages 1-1
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    2. Numbers and Functions

      • Serge Lang
      Pages 3-20

    3. Graphs and Curves

      • Serge Lang
      Pages 21-54

  3. Differentiation and Elementary Functions

    1. Front Matter

      Pages 55-55
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    2. The Derivative

      • Serge Lang
      Pages 57-116

    3. Sine and Cosine

      • Serge Lang
      Pages 117-158

    4. The Mean Value Theorem

      • Serge Lang
      Pages 159-180

    5. Sketching Curves

      • Serge Lang
      Pages 181-215

    6. Inverse Functions

      • Serge Lang
      Pages 216-235

    7. Exponents and Logarithms

      • Serge Lang
      Pages 236-283

  4. Integration

    1. Front Matter

      Pages 285-285
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    2. Integration

      • Serge Lang
      Pages 287-311

    3. Properties of the Integral

      • Serge Lang
      Pages 312-334

    4. Techniques of Integration

      • Serge Lang
      Pages 335-378

    5. Applications of Integration

      • Serge Lang
      Pages 379-423

  5. Taylor’s Formula and Series

    1. Front Matter

      Pages 425-425
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    2. Taylor’s Formula

      • Serge Lang
      Pages 427-472

    3. Series

      • Serge Lang
      Pages 473-500

  6. Functions of Several Variables

    1. Front Matter

      Pages 521-521
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: A First Course in Calculus

  • Authors: Serge Lang

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-8532-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1986

  • Hardcover ISBN: 978-0-387-96201-6Published: 15 January 1986

  • Softcover ISBN: 978-1-4612-6428-6Published: 13 September 2012

  • eBook ISBN: 978-1-4419-8532-3Published: 17 September 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 5

  • Number of Pages: XV, 731

  • Additional Information: Originally published by Addison-Wesley Publishing Company, 1978, 1973, 1968, 1964

  • Topics: Real Functions

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