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Qu’il s’agisse d’applications en physique ou en mécanique, en médecine ou en biologie, mais aussi en économie, dans les médias et en marketing, ou encore dans le domaine des finances, la traduction phénoménologique du système étudié conduit très souvent à la résolution d’équations différentielles ou aux dérivées partielles. Incontestablement, ce sont les éléments finis qui ont bouleversé le monde de l’approximation numérique des équations aux dérivées partielles. Cet ouvrage est composé de deux parties : la première est un abrégé de cours portant sur les outils de base de l’analyse mathématique des équations aux dérivées partielles et la seconde contient des problèmes corrigés qui abordent l’approximation par éléments finis des formulations variationnelles des problèmes aux limites elliptiques. Des applications en mécanique des solides déformables, à la résistance des matériaux, en mécanique des fluides et en thermique ainsi que quelques problèmes non linéaires y sont présentés.Cet ouvrage s'adresse aux étudiants en sciences et techniques de l'ingénieur des universités et des grandes écoles.
This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite-element methods instead of passively absorbing the material, as in most standard textbooks. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used. Furthermore, an introduction to tensor calculus using distribution theory offers further insight for readers with different mathematical backgrounds.
Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par tial differential equations with boundary conditions. He studied singulari ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before.
Scientific and technical contacts between nations· have necessitated the publication of various language textbooks, manuals and reference books. Particularly important among them are multilingual scientifio and technical dictionaries. This English-German-French-Dutch-Russian Dictionary of Scientifio and Technical Terms contains some 9000 entries. The main fea ture of the Dictionary is that it includes first and foremost general scientific terms needed by an engineer working in any branch of science and technology. Besides, the Dictionary includes the basic terms used in physics, mathemat ics, the fundamentals of electrical engineering and chemistry, and also the most essential terms pertaining to manufacturing processes. machine design, testing methods, etc. The Compilers were confronted with a difficult task, as nowadays science and technology are developing rapidly and the minimum scientific and tech nical vocabulary required by a specialist is increasing accordingly. The Compilers have taken special pains to include the entire basic mod ern technical vocabulary, omitting superfluous words and phrases. They have tried to solve this problem by selecting mainly those scientific and tech nical terms which constitute the basic of a specialised vocabulary. There fore, the Dictionary includes the vocabulary pertaining to general study courses in mathematics, physics and chemistry, and also in electrical engi neering. electronics and machine design, given in technical colleges irrespect ive of their specification. This lends the Dictionary an «all-purpose» char acter, making it equally useful to scientists and engineers of different countries, who have graduated from colleges with different curricula.
Includes Part 1, Number 1: Books and Pamphlets, Including Serials and Contributions to Periodicals (January - June)
Inland & Maritime Waterways & Ports: Design, Construction, and Operation covers the proceedings of the technical sessions in the 25th Permanent International Association of Navigation Congress, held in Scotland. This book is organized into two sections encompassing 10 chapters. The first section deals first with means for the protection of banks and bottom waterways against the attack by currents and waves, including those generated by ships. These topics are followed by discussions on methods of increasing waterways capacity and safety; sedimentation reduction and improving and maintaining navigable depths in alluvial channels; integration of ocean-coastal-inland navigation; and improvements of maritime ports and inland terminals. The second section starts with discussions of the developments in the construction of ships, navigational aids, waterways and harbors, traffic management and installations, with particular emphasis on risk analysis and safety criteria regarding transportation, unloading, and storage of liquefied natural and petroleum gases. Other topics covered in this section include economic optimization of the whole dredging cycle; cargo handling systems and equipment; design and construction of port facilities and arrangement of quay platforms; and coastal erosion caused by harbor works and corrective measures. This book will prove useful to design and navigation engineers and researchers.
Le réel est (réellement) non représentable: telle est la découverte majeure que les scientifiques et les physiciens en particulier, ont faite pour leur compte au cours du XXe siècle. Mais, le savent-ils? The real is (really) unrepresentable: this is the major discovery that scientists and physicists in particular have made on their own during the twentieth century.