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Mathematical Analysis II (Second Edition)книга
- Автор: Zorich Vladimir A.
- Год издания: 2016
- Место издания: Springer Heidelberg, New York, Dordrecht, London
- Объём: 720 страниц
- ISBN: 978-3-662-48991-8
- Учебник
- DOI: 10.1007/978-3-662-48993-2
- Аннотация: MATHEMATICAL ANALYSIS II This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading to its advanced topics. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first and five of them in the second volume. Some of the appendices are surveys, both prospective and retrospective. The final survey contains the most important conceptual achievements of the whole course, which establish connections of analysis with other parts of mathematics. This second volume presents classical analysis as it is courant form as a part of unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions. “The textbook of Zorich seems to me the most successful of the available comprehensive textbooks of analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways: on the one hand in its closer relation to natural-science applications (primarily to physics and mechanics) and on the other hand in a greater-than-usual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and the elements of the theory of asymptotic expansions. At present such a way of structuring the course must be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses, noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere logical justifications. The need to return to more substantive courses of analysis now seems obvious, especially in connection with the applied character of the future activity of the majority of students. ...In my opinion, this course is the best of the existing modern courses of analysis.” From a review by V.I.Arnold
- Добавил в систему: Зорич Владимир Антонович