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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.
V.1. A.N. v.2. O.Z. Apendices and indexes.
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
This book offers a unique compilation of papers in mathematics and physics from Freeman Dyson's 50 years of activity and research. These are the papers that Dyson considers most worthy of preserving, and many of them are classics. The papers are accompanied by commentary explaining the context from which they originated and the subsequent history of the problems that either were solved or left unsolved. This collection offers a connected narrative of the developments in mathematics and physics in which the author was involved, beginning with his professional life as a student of G. H. Hardy.
This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field
Clair et didactique, ce manuel de référence aide à comprendre et assimiler les principes fondamentaux des différentes méthodes électrochimiques les plus utilisées dans le domaine de l'analyse chimique. Reposant sur une démarche progressive et enrichi de nombreux exemples d'application, il se compose de trois parties proposant : un rappel des concepts généraux de l'électrochimie : cellules électrochimiques, interfaces, courbes intensité-potentiel, transferts de charge, électrolyse , une étude détaillée des méthodes électrochimiques d'analyse : polarographie, voltammétrie, ampérométrie, conductométrie, potentiométrie, coulométrie, biocapteurs et détecteurs électrochimiques, des développements théoriques complémentaires établissant les relations mathématiques qui constituent le fondement des applications des méthodes précédentes. Méthodes électrochimiques d'analyse s'adresse à tous les praticiens de l'analyse chimique : pharmaciens hospitaliers, techniciens et ingénieurs dans le domaine pharmaceutique, praticiens et techniciens de laboratoire d'analyses médicales. Par son parti pris pédagogique, cet ouvrage est également destiné aux étudiants de chimie de tous les niveaux universitaires ainsi qu'à ceux préparant les grandes écoles d'ingénieurs et scientifiques d'horizons divers.