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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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Table of contents (11 chapters)
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Front Matter
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Linear Algebra
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Front Matter
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Metrics and Topology
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Front Matter
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Continuity in Infinite-Dimensional Spaces
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Front Matter
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Back Matter
About this book
Reviews
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)
Authors and Affiliations
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Dipartimento di Matematica, Scuola Normale Superiore, Pisa, Italy
Mariano Giaquinta
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Dipartimento di Matematica Applicata, Università degli Studi di Firenze, Firenze, Italy
Giuseppe Modica
Bibliographic Information
Book Title: Mathematical Analysis
Book Subtitle: Linear and Metric Structures and Continuity
Authors: Mariano Giaquinta, Giuseppe Modica
DOI: https://doi.org/10.1007/978-0-8176-4514-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2007
Hardcover ISBN: 978-0-8176-4374-4Published: 14 March 2007
Softcover ISBN: 978-0-8176-4375-1Published: 04 September 2007
eBook ISBN: 978-0-8176-4514-4Published: 08 October 2007
Edition Number: 1
Number of Pages: XX, 466
Topics: Analysis, Ordinary Differential Equations, Topology, Functional Analysis, Real Functions, Applications of Mathematics