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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 presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book.
Unique en son genre dans sa conception et dans son contenu, Labo-Stat - Guide de validation des méthodes d'analyses présente une nouvelle stratégie de validation selon une démarche raisonnée fondée sur le profil d'exactitude. Les techniques statistiques adaptées y sont explicitées sous une forme didactique et les solutions possibles ainsi que les limites éventuelles de diverses normes existantes sont largement développées et illustrées d'exemples concrets directement exploitables. Les applications numériques, sous forme de feuilles de calcul modèles pour des tableurs et des petits scripts, sont téléchargeables en ligne. Complétée par les explications de cet ouvrage, elles permettent au non-statisticien d'accéder aisément à une interprétration graphique des résultats. Labo-Stat a été conçu pour pouvoir être facilement utilisé sur la paillasse du laboratoire et permettre à tout un chacun, responsable, ingénieur, chercheur, technicien ou étudiant, de s'approprier les techniques indispensables pour déboucher sur une conclusion claire et sans ambiguïté et mener la validation des méthodes dans un souci de contrôle des coûts.
‘Love is harder to explain than hunger, for a piece of fruit does not feel the desire to be eaten’: Denis Diderot’s Éléments de physiologie presents a world in flux, turning on the relationship between man, matter and mind. In this late work, Diderot delves playfully into the relationship between bodily sensation, emotion and perception, and asks his readers what it means to be human in the absence of a soul. The Atheist’s Bible challenges prevailing scholarly views on Diderot’s Éléments, asserting its contemporary philosophical importance, and prompting its readers to inspect more closely this little-known and little-studied work. In this timely volume, Warman establishes the place of Diderot’s Éléments in the trajectory of materialist theories of nature and the mind stretching back to Epicurus and Lucretius, and explores the fascinating reasons behind scholarly neglect of this seminal work. In turn, Warman outlines the hitherto unacknowledged dissemination and reception of Diderot’s Éléments, demonstrating how Diderot’s Éléments was circulated in manuscript-form as early as the 1790s, thus showing how the text came to influence the next generations of materialist thinkers. This book is accompanied by a digital edition of Jacques-André Naigeon’s Mémoires historiques et philosophiques sur la vie et les ouvrages de Denis Diderot (1823), a work which, Warman argues, represents the first publication of Diderot’s Éléments, long before its official publication date of 1875. The Atheist’s Bible constitutes a major contribution to the field of Diderot studies, and will be of further interest to scholars and students of materialist natural philosophy in the Age of Enlightenment and beyond.
V.1. A.N. v.2. O.Z. Apendices and indexes.
Origin and Distribution of the Elements, Volume 30 presents detailed studies of trace elements and isotopes and the use of these data with the techniques of physical and organic chemistry to make relevant interpretations in geology. This book discusses some of the problems of applied chemistry. Organized into five sections encompassing 89 chapters, this volume begins with an overview of the theories of nucleosynthesis that are based on broad empirical foundations involving experiment in nuclear physics and observation in geophysics and astronomy. This text then explores the primeval abundance of the elements wherein the composition of the material from which the Galaxy is formed. Other chapters consider the production of helium in the galaxy. This book discusses as well the dynamics of the cores of highly evolved massive stars. The final chapter deals with the measurements of site populations in crystal structures by electron diffraction and X-ray. Physicists, astronomers, geologists, and geochemists will find this book extremely useful.
The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.
This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.