Mathematical Analysis

From the reviews: "This book is suitable as a text for graduate students. Photographs of Banach, Frechet, 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. Kerchy, 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 Medkova, 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 fur Mathematik, Vol. 157 (2), June, 2009)

• 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.