Calculus Without Limits
Calculus Without Limits by Giuseppe Furnari, published by Lulu.com on March 24, 2010, is a 104-page exploration of the historical development of calculus concepts. This edition delves into the contributions of classical Greek mathematicians like Euclid and Archimedes, highlighting their early ideas that paved the way for infinitesimal and integral calculus. The author discusses the evolution of these concepts through figures such as Leibniz and Newton, addressing the logical challenges posed by infinitesimals and the subsequent resolutions proposed by mathematicians like Weierstrass and Robinson.
Readers will find a thorough examination of the historical context surrounding calculus, focusing on the classical methodology that makes complex ideas more accessible. The book presents a clear narrative on how the concept of infinitesimals has been understood and refined over time, emphasizing the importance of logical consistency in mathematical theory. By adopting a straightforward approach, this work aims to clarify the intricacies of calculus for those interested in the scientific foundations of mathematics.
Official synopsis Publisher
The Greek of the classical age, with Euclid and Archimedes, have conceived very next ideas to those that have allowed the invention of the Infinitesimal and Integral calculation. The author thinks how just Euclide has grazed the concept of infinitesimal, with his theorem related to the “horn angle”. It was then in 1600 that Leibniz and Newton they created the Infinitesimal Calculus and that Integral. But the infinitesimals have always elicited criticisms for their logical contradictions, immediately stigmatized by the bishop Berkeley. With the method of the double limit of Weierstrass, the problem apparently, seems overcome. Then in the 1900 Robinson overcome the impasse from the logical point of view, but resorting to the Analysis not-standard, in the sphere of not Archimedean fields. With this work the author overcomes the issue of the infinitesimals, adopting a very classical methodology and, above all, of easy understanding.
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