Mathematical Analysis : Linear and Metric Structures and Continuity PDF
by Mariano Giaquinta, Giuseppe Modica
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].
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Download - Immediately Available
- Format:PDF
- Publisher:Birkhauser Boston
- Publication Date:08/10/2007
- Category:
- ISBN:9780817645144
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Information
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Download - Immediately Available
- Format:PDF
- Publisher:Birkhauser Boston
- Publication Date:08/10/2007
- Category:
- ISBN:9780817645144
