MARC details
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04830nam a22005175i 4500 |
| 001 - CONTROL NUMBER |
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978-0-387-73468-2 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20160302163237.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2008 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387734682 |
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978-0-387-73468-2 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-0-387-73468-2 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA21-27 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBX |
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bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT015000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510.9 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Ferraro, Giovanni. |
| Relator term |
author. |
| 245 14 - TITLE STATEMENT |
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| Title |
The Rise and Development of the Theory of Series up to the Early 1820s |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Giovanni Ferraro. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2008. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XVI, 392 p. 21 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Sources and Studies in the History of Mathematics and Physical Sciences |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
From the beginnings of the 17th century to about 1720: Convergence and formal manipulation -- Series before the rise of the calculus -- Geometrical quantities and series in Leibniz -- The Bernoulli series and Leibniz’s analogy -- Newton’s method of series -- Jacob Bernoulli’s treatise on series -- The Taylor series -- Quantities and their representations -- The formal-quantitative theory of series -- The first appearance of divergent series -- From the 1720s to the 1760s: The development of a more formal conception -- De Moivre’s recurrent series and Bernoulli’s method -- Acceleration of series and Stirling’s series -- Maclaurin’s contribution -- The young Euler between innovation and tradition -- Euler’s derivation of the Euler–Maclaurin summation formula -- On the sum of an asymptotic series -- Infinite products and continued fractions -- Series and number theory -- Analysis after the 1740s -- The formal concept of series -- The theory of series after 1760: Successes and problems of the triumphant formalism -- Lagrange inversion theorem -- Toward the calculus of operations -- Laplace’s calculus of generating functions -- The problem of analytical representation of nonelementary quantities -- Inexplicable functions -- Integration and functions -- Series and differential equations -- Trigonometric series -- Further developments of the formal theory of series -- Attempts to introduce new transcendental functions -- D’Alembert and Lagrange and the inequality technique -- The decline of the formal theory of series -- Fourier and Fourier series -- Gauss and the hypergeometric series -- Cauchy’s rejection of the 18th-century theory of series. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Functions of real variables. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Sequences (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
History. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
History of Mathematical Sciences. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Sequences, Series, Summability. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Real Functions. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Analysis. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9780387734675 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Sources and Studies in the History of Mathematics and Physical Sciences |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-0-387-73468-2">http://dx.doi.org/10.1007/978-0-387-73468-2</a> |
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ZDB-2-SMA |
