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Table of contents

  1. Front Matter
    Pages I-XV
  2. From the beginnings of the 17th century to about 1720: Convergence and formal manipulation

    1. Front Matter
      Pages 1-2
    2. Giovanni Ferraro
      Pages 3-24
    3. Giovanni Ferraro
      Pages 25-44
    4. Giovanni Ferraro
      Pages 45-51
    5. Giovanni Ferraro
      Pages 53-78
    6. Giovanni Ferraro
      Pages 79-85
    7. Giovanni Ferraro
      Pages 87-92
    8. Giovanni Ferraro
      Pages 93-113
    9. Giovanni Ferraro
      Pages 115-120
    10. Giovanni Ferraro
      Pages 121-130
  3. From the 1720s to the 1760s: The development of a more formal conception

    1. Front Matter
      Pages 131-132
    2. Giovanni Ferraro
      Pages 141-146
    3. Giovanni Ferraro
      Pages 147-153
    4. Giovanni Ferraro
      Pages 155-169
    5. Giovanni Ferraro
      Pages 181-184
    6. Giovanni Ferraro
      Pages 185-192
    7. Giovanni Ferraro
      Pages 193-199
    8. Giovanni Ferraro
      Pages 201-214
    9. Giovanni Ferraro
      Pages 215-229
  4. The theory of series after 1760: Successes and problems of the triumphant formalism

    1. Front Matter
      Pages 231-231
    2. Giovanni Ferraro
      Pages 233-237
    3. Giovanni Ferraro
      Pages 239-244
    4. Giovanni Ferraro
      Pages 245-250
    5. Giovanni Ferraro
      Pages 257-262
    6. Giovanni Ferraro
      Pages 263-265
    7. Giovanni Ferraro
      Pages 267-274
    8. Giovanni Ferraro
      Pages 275-282
  5. The decline of the formal theory of series

    1. Front Matter
      Pages 311-313
    2. Giovanni Ferraro
      Pages 315-322
    3. Giovanni Ferraro
      Pages 323-345
  6. Back Matter
    Pages 363-389

About this book

Introduction

The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians.

 

This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today.

 

Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise.

Keywords

Fourier series Taylor series calculus differential equation number theory

Authors and affiliations

  • Giovanni Ferraro
    • 1
  1. 1.Dipartimento STATUniversità del Molise86090 PescheItaly

Bibliographic information