Mariano Giaquinta, Giuseppe Modica

Mathematical Analysis

Linear and Metric Structures and Continuity

• Broschiertes Buch

Produktbeschreibung

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 shall refer to as [GM1] and in M. G- quinta, G. Modica, Mathematical Analysis. Approximation and Discrete Processes, Birkhs Boston, 2004, which we shall refer to as [GM2].

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Produktdetails

• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 11018964, 978-0-8176-4375-1
• 2007
• Seitenzahl: 488
• Erscheinungstermin: 4. September 2007
• Englisch
• Abmessung: 235mm x 155mm x 27mm
• Gewicht: 778g
• ISBN-13: 9780817643751
• ISBN-10: 0817643753
• Artikelnr.: 20791859

Autorenporträt

Mariano Giaquinta, Scuola Normale Superiore, Pisa, Italy / Giuseppe Modica, Università degli Studi di Firenze, Italy

Inhaltsangabe

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.

Rezensionen

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 topologyfor 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)