Mathematical Analysis: Linear and Metric Structures and Continuity / Edition 1

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Overview

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 equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index

May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers

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Editorial Reviews

From the Publisher

From the reviews:

"This book is suitable as a text for graduate students. Photographs of Banach, Fréchet, Hausdorff, Hilbert and some others mathematicians are imprinted in order to involve [the reader] in the work of mathematicians."—Zentralblatt MATH

"This volume is an English translation and revised edition of a former Italian version published in 2000. … This nice book is recommended to advanced undergraduate and graduate students. It can serve also as a valuable reference for researchers in mathematics, physics, and engineering." (L. Kérchy, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

“The book ‘M. Giaquinta, G. Modica: Mathematical Analysis. Linear and Metric Structures and Continuity’ is a lovely book which should be in the bookcase of every expert in mathematical analysis.” (Dagmar Medková, Mathematica Bohemica, Issue 2, 2010)

“This book offers a self-contained introduction to certain central topics of functional analysis and topology for advanced undergraduate and graduate students. … the clear and self-contained style recommend the book for self-study, offering a quick introduction to a number of central notions of functional analysis and topology. A large number of exercises and historical remarks add to the pleasant overall impression the book leaves.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)

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Product Details

  • ISBN-13: 9780817643744
  • Publisher: Birkhauser Verlag
  • Publication date: 3/14/2007
  • Edition description: 2007
  • Edition number: 1
  • Pages: 466
  • Product dimensions: 9.00 (w) x 6.00 (h) x 1.25 (d)

Table of Contents

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.

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