| Mathematical Analysis: Linear and Metric Structures and Continuity Contributor(s): Giaquinta, Mariano (Author), Modica, Giuseppe (Author) |
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ISBN: 0817643745 ISBN-13: 9780817643744 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: March 2007 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Algebra - Linear - Mathematics | Functional Analysis |
| Dewey: 515 |
| LCCN: 2006927565 |
| Physical Information: 1.1" H x 6.2" W x 9.2" (1.76 lbs) 466 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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]. |