Introductory Functional Analysis

ISBN-13: 9780387983073 / Angielski / Twarda / 1997 / 472 str.

B. Daya Reddy; L. Sirovich; J. E. Marsden

Opis

Mathematics is playing an ever more important role in the physical and biological sciences, provo king a blurring of boundaries between scientific dis- ciplines and a resurgence of interest in the modern as weil as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathe- matics (TAM). The development of new courses is a natural consequence of a . high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable fur use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A proper understanding of the theory of boundary value problems, as op- posed to a knowledge of techniques for solving specific problems or classes of problems, requires some background in functional analysis.

Spis treści

Contents.- Introduction.- Linear Functional Analysis.- Sets.- The algebra of sets.- Sets of numbers.- Rn and its subsets.- Relations, equivalence classes and Zorn's lemma.- Theorem-proving.- Bibliographical remarks.- Exercises.- Sets of functions and Lebesgue integration.- Continuous functions.- Meansure of sets in Rn.- Lebesgue integration and the space Lp(_).- Bibliographical remarks .- Exercises.- Vector spaces, normed and inner product spaces.

Blurb

THIS IS BOTH PROMO COPY AND BACK COVER COPY!!!!! This book provides an introduction to functional analysis and treats in detail its application to boundary-value problems and finite elements. The book is intended for use by senior undergraduate and graduate students in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis would also find the text useful. The text is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. Readers of this book can expect to obtain a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.