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In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d analyse. For this translation, the authors have also added commentary, notes, references, and an index.
The year 2007 marks the 300th anniversary of the birth of one of
the Enlightenment's most important mathematicians and scientists,
Leonhard Euler. This volume is a collection of 24 essays by some of
the world's best Eulerian scholars from seven different countries
about Euler, his life and his work.
This monograph is an annotated translation of what is considered to be the world's first calculus textbook, originally published in French in 1696. That anonymously published textbook on differential calculus was based on lectures given to the Marquis de l'Hopital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulli's lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulli's notes, in Latin, to l'Hopital's text in French. The similarities are remarkable, but there is also much in l'Hopital's book that is original and innovative. This book offers the first English translation of Bernoulli's notes, along with the first faithful English translation of l'Hopital's text, complete with annotations and commentary. Additionally, a significant portion of the correspondence between l'Hopital and Bernoulli has been included, also for the fi rst time in English translation. This translation will provide students and researchers with direct access to Bernoulli's ideas and l'Hopital's innovations. Both enthusiasts and scholars of the history of science and the history of mathematics will fi nd food for thought in the texts and notes of the Marquis de l'Hopital and his teacher, Johann Bernoulli.
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