# Mathematical Analysis: Linear and Metric Structures and Continuity

Springer Science & Business Media, Sep 4, 2007 - Mathematics - 466 pages
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].

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 II 2 IV 3 VI 10 VII 22 VIII 31 IX 37 X 40 XII 57
 XXXV 247 XXXVI 249 XXXVII 250 XXXVIII 272 XXXIX 281 XL 283 XLI 284 XLIII 295

 XIII 76 XIV 79 XV 95 XVI 109 XVII 111 XIX 128 XX 143 XXI 146 XXII 147 XXIII 151 XXIV 174 XXV 185 XXVI 190 XXVII 197 XXIX 205 XXX 210 XXXI 216 XXXII 218 XXXIV 241
 XLIV 303 XLV 322 XLVI 334 XLVII 344 XLVIII 351 L 363 LI 368 LII 378 LIII 393 LIV 395 LVI 402 LVII 403 LVIII 424 LIX 431 LX 455 LXI 457 LXII 458 Copyright