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Introduction to Analysis of the Infinite

Book I

  • Book
  • © 1988

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Authors:
  1. Euler
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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. On Functions in General

    • Euler
    Pages 2-16

  3. On the Transformation of Functions

    • Euler
    Pages 17-37

  4. On the Transformation of Functions by Substitution

    • Euler
    Pages 38-49

  5. On the Development of Functions in Infinite Series

    • Euler
    Pages 50-63

  6. Concerning Functions of Two or More Variables

    • Euler
    Pages 64-74

  7. On Exponentials and Logarithms

    • Euler
    Pages 75-91

  8. Exponentials and Logarithms Expressed through Series

    • Euler
    Pages 92-100

  9. On Transcendental Quantities Which Arise from the Circle

    • Euler
    Pages 101-115

  10. On Trinomial Factors

    • Euler
    Pages 116-136

  11. On the Use of the Discovered Factors to Sum Infinite Series

    • Euler
    Pages 137-153

  12. On Other Infinite Expressions for Arcs and Sines

    • Euler
    Pages 154-168

  13. On the Development of Real Rational Functions

    • Euler
    Pages 169-180

  14. On Recurrent Series

    • Euler
    Pages 181-203

  15. On the Multiplication and Division of Angles

    • Euler
    Pages 204-227

  16. On Series Which Arise From Products

    • Euler
    Pages 228-255

  17. On the Partition of Numbers

    • Euler
    Pages 256-282

  18. Using Recurrent Series to Find Roots of Equations

    • Euler
    Pages 283-302

  19. On Continued Fractions

    • Euler
    Pages 303-327
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Keywords

About this book

From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Bibliographic Information

  • Book Title: Introduction to Analysis of the Infinite

  • Book Subtitle: Book I

  • Authors: Euler

  • DOI: https://doi.org/10.1007/978-1-4612-1021-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-387-96824-7Published: 21 September 1988

  • Softcover ISBN: 978-1-4612-6988-5Published: 21 March 2013

  • eBook ISBN: 978-1-4612-1021-4Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XV, 327

  • Additional Information: Title of the original Latin edition: Introductio in analysin infinitorum

  • Topics: Real Functions

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