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].
Reviews

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)

Book Information
ISBN 9780817643744
Author Mariano Giaquinta
Format Hardback
Page Count 466
Imprint Birkhauser Boston Inc
Publisher Birkhauser Boston Inc