| Mathematical Analysis: Linear and Metric Structures and Continuity 2007 Edition Contributor(s): Giaquinta, Mariano (Author), Modica, Giuseppe (Author) |
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ISBN: 0817643753 ISBN-13: 9780817643751 Publisher: Birkhauser OUR PRICE: $80.74 Product Type: Paperback - Other Formats Published: September 2007 Annotation: This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Differential Equations - General - Mathematics | Topology - General |
| Dewey: 515 |
| Physical Information: 0.86" H x 6.35" W x 9.23" (1.34 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]. |