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Titlebook: Mathematical Analysis; Linear and Metric St Mariano Giaquinta,Giuseppe Modica Textbook 2007 Birkh?user Boston 2007 calculus.compactness.dif

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書目名稱Mathematical Analysis
副標(biāo)題Linear and Metric St
編輯Mariano Giaquinta,Giuseppe Modica
視頻videohttp://file.papertrans.cn/626/625957/625957.mp4
概述Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level.Includes applications to geometry and differential equati
圖書封面Titlebook: Mathematical Analysis; Linear and Metric St Mariano Giaquinta,Giuseppe Modica Textbook 2007 Birkh?user Boston 2007 calculus.compactness.dif
描述One of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system. We have already discussed real functions of one real variable and a few examples of functions of several variables but there are many more examples of functions that the real world, physics, natural and social sciences, and mathematics have to offer: (a) not only do we associate numbers and points to points, but we as- ciate numbers or vectors to vectors, (b) in the calculus of variations and in mechanics one associates an - ergy or action to each curve y(t) connecting two points (a, y(a)) and (b,y(b)): b Lea ~(y) - / 9 F(t, y(t), y‘ (t))dt t. J a in terms of the so-called Lagrangian F(t, y, p), (c) in the theory of integral equations one maps a function into a new function b /1, d-r / o. J a by means of a kernel K(s, T), (d) in the theory of differential equations one considers transformations of a function x(t) into the new function t t f f( a where f(s, y) is given. 1 in M. Giaquinta, G. Modica, Mathematical Analysis. Functions of One Va- able, Birkh~user, Boston, 2003, which we sha
出版日期Textbook 2007
關(guān)鍵詞calculus; compactness; differential equation; self-adjoint operators; spectral theorem; topology of metri
版次1
doihttps://doi.org/10.1007/978-0-8176-4514-4
isbn_softcover978-0-8176-4375-1
isbn_ebook978-0-8176-4514-4
copyrightBirkh?user Boston 2007
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板凳
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Self-Adjoint OperatorsIn this chapter, we deal with self-adjoint operators on a Euclidean or Hermitian space, and, more precisely, with the spectral theory for self-adjoint and normal operators. In the last section, we shall see methods and results of linear algebra at work on some specific examples and problems.
地板
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Compactness and ConnectednessIn this chapter we shall discuss, still in the metric context, two important topological invariants: . and ..
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Mariano Giaquinta,Giuseppe ModicaExamines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level.Includes applications to geometry and differential equati
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Curvescurves as geometric figures characterized by specific geometric properties, as the conics, and the heritage of the XVIII century, when, with the development of mechanics, curves were thought of as the trace of a moving point.
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發(fā)表于 2025-3-23 04:27:27 | 只看該作者
Hilbert Spaces, Dirichlet’s Principle and Linear Compact Operators Banach space whose norm is induced by an inner (or Hermitian) product. The inner (Hermitian) product allows us to measure the length of a vector, the distance between two vectors and the angle formed by them.
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發(fā)表于 2025-3-23 07:28:36 | 只看該作者
el.Includes applications to geometry and differential equatiOne of the fundamental ideas of mathematical analysis is the notion of a function; we use it to describe and study relationships among variable quantities in a system and transformations of a system. We have already discussed real functions
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