NDLI: Geometry and analysis in Euler’s integral calculus

Content Provider	Springer Nature Link
Author	Capobianco, Giovanni Enea, Maria Rosaria Ferraro, Giovanni
Copyright Year	2016
Abstract	Euler developed a program which aimed to transform analysis into an autonomous discipline and reorganize the whole of mathematics around it. The implementation of this program presented many difficulties, and the result was not entirely satisfactory. Many of these difficulties concerned the integral calculus. In this paper, we deal with some topics relevant to understand Euler’s conception of analysis and how he developed and implemented his program. In particular, we examine Euler’s contribution to the construction of differential equations and his notion of indefinite integrals and general integrals. We also deal with two remarkable difficulties of Euler’s program. The first concerns singular integrals, which were considered as paradoxical by Euler since they seemed to violate the generality of certain results. The second regards the explicitly use of the geometric representation and meaning of definite integrals, which was gone against his program. We clarify the nature of these difficulties and show that Euler never thought that they undermined his conception of mathematics and that a different foundation was necessary for analysis.
Starting Page	1
Ending Page	38
Page Count	38
File Format	PDF
ISSN	00039519
Journal	Archive for History of Exact Sciences
Volume Number	71
Issue Number	1
e-ISSN	14320657
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-05-12
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	History of Mathematical Sciences Philosophy of Science History of Science Mathematics Astronomy, Observations and Techniques History and Philosophical Foundations of Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics History and Philosophy of Science

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