Excursus into the History of Calculus

This paper describes the evolution of aspects of differential and algebraic gometry from the mid 17th century till the end of the 18th century.

This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon Newton's approach to differential equations. Then the development of the various methods for solving the first order differential equations and the second order linear differential equations are discussed. The paper concludes with a brief me...

This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.

This is a overview of the genesis of epsilon-delta language in works of mathematicians of the 19th century. It shows that although the symbols epsilon and delta were initially introduced in 1823 by Cauchy, no functional relationship for delta as a function of epsilon was ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass' definition of a limit. The article gives various interpretations of these issues later...

An alternative organization for Differential and Integral Calculus, based on an extension of real numbers that include infinitesimal and infinite quantities, is presented. Only Elementary Set Theory is used, without reference to methods or results from Mathematical Logic.

This is the translation of Euler's Latin textbook Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum (second volume) into English.

This article has his origin in some lectures given at the University of Bologna, inside an interdisciplinary program of mathematics, history of science, physics and philosophy. Since they are at the junction of these fields, movement and infinitesimal calculus are good instances to understand some fundamental questions in history of sciences, the diversity of the conceptions stretching across it and more generally the philosophy background of theses researches. It is the fiel...

An exposition of smooth infinitesimal analysis, which is a way to do calculus with nilsquare infinitesimals, is given.

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and...

This paper has been withdrawn by the author.