Springer copernicus jun 1984 (2 Ergebnisse)
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an app…aratus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given 'surfaces' in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 164 pp. Englisch.
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -These notes are the contents of a one semester graduate course which taught at Brown University during the academic year 1981-1982. They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, i…n the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle. Very little background is needed to read these notes. The main re sults of functional analysis which are used here are recalled in the text. The goal of the two first chapters is to introduce the notion of Varia tional Inequality and give some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problems. These problems have now invaded a large domain of applied mathematics including optimal control theory and mechanics, and a collec tion of regularity results available seems to be timely. Roughly speaking, for elliptic variational inequalities of second order we prove that the solution has as much regularity as the obstacle(s). We combine here the theory for one or two obstacles in a unified way, and one of our hopes is that the reader will enjoy the wide diversity of techniques used in this approach. The fourth chapter is concerned with the dam problem. This problem has been intensively studied during the past decade (see the books of Baiocchi-Capelo and Kinderlehrer-Stampacchia in the references). The relationship with Variational Inequalities has already been quoted above.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 132 pp. Englisch.
