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Analysis, manifolds and physics - Choquet-Bruhat Y., Dewitt-Morette C., Dillard-Bleick M.

Название: Analysis, manifolds and physics
Автор: Choquet-Bruhat Y., Dewitt-Morette C., Dillard-Bleick M.
Категория: Физика
Тип: Книга
Дата: 21.10.2008 20:25:56
Скачано: 146
Описание: All too often in physics familiarity is a substitute for understanding, and the beginner who lacks familiarity wonders which is at fault: physics or himself. Physical mathematics provides well defined concepts and techniques for the study of physical systems. It is more than mathematical techniques used in the solution of problems which have already been formulated; it helps in the very formulation of the laws of physical systems and brings a better understanding of physics. Thus physical mathematics includes mathematics which gives promise of being useful in our analysis of physical phenomena. Attempts to use mathematics for this purpose may fail because the mathematical tool is too crude; physics may then indicate along which lines it should be sharpened. In fact, the analysis of physical systems has spurred many a new mathematical development. Considerations of relevance to physics underlie the choice of material included here. Any choice is necessarily arbitrary; we included first the topics which we enjoy most but we soon recognized that instant gratification is a short range criterion. We then included material which can be appreciated only after a great deal of intellectual asceticism but which may be farther reaching. Finally, this book gathers the starting points of some great currents of contemporary mathematics. It is intended for an advanced physical mathematics course. Chapters I and II are two preliminary chapters included here to spare the reader the task of looking up in several specialized books the definitions and the basic theorems used in the subsequent chapters. Chapter I is merely a review of fundamental notions of algebra, topology, integration, and analysis. Chapter II treats the essentials of differential calculus and calculus of variations on Banach spaces. Each of the following chapters introduces a mathematical structure and exploits it until it is sufficiently familiar to become an "instrument de pensee"1: Chapter III, differentiable manifolds, tangent bundles and their use in Lie groups; Chapter IV, exterior derivation and the solutions of exterior differential systems; Chapter V, Riemannian structures which, together with the previous structures provide the basic geometric notions needed in physics; Chapter VI, distributions and the Sobolev spaces with recent applications to the theory of partial differential equations.
Файл: 3.84 МБ