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＜電子ブック＞
Mathematical Analysis : Linear and Metric Structures and Continuity / by Mariano Giaquinta, Giuseppe Modica

版	1st ed. 2007.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2007
本文言語	英語
大きさ	XX, 466 p : online resource
著者標目	*Giaquinta, Mariano author Modica, Giuseppe author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Differential equations LCSH:Topology LCSH:Functional analysis LCSH:Functions of real variables LCSH:Mathematics FREE:Analysis FREE:Differential Equations FREE:Topology FREE:Functional Analysis FREE:Real Functions FREE:Applications of Mathematics
一般注記	Linear Algebra -- Vectors, Matrices and Linear Systems -- Vector Spaces and Linear Maps -- Euclidean and Hermitian Spaces -- Self-Adjoint Operators -- Metrics and Topology -- Metric Spaces and Continuous Functions -- Compactness and Connectedness -- Curves -- Some Topics from the Topology of ?n -- Continuity in Infinite-Dimensional Spaces -- Spaces of Continuous Functions, Banach Spaces and Abstract Equations -- Hilbert Spaces, Dirichlet’s Principle and Linear Compact Operators -- Some Applications This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis HTTP:URL=https://doi.org/10.1007/978-0-8176-4514-4

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