B. D. Reddy

Introductory Functional Analysis

With Applications to Boundary Value Problems and Finite Elements

• Broschiertes Buch

Produktbeschreibung

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 für 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.

Produktdetails

• Texts in Applied Mathematics 27
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4612-6824-6
• Softcover reprint of the original 1st ed. 1998
• Seitenzahl: 488
• Erscheinungstermin: 20. November 2013
• Englisch
• Abmessung: 235mm x 155mm x 27mm
• Gewicht: 741g
• ISBN-13: 9781461268246
• ISBN-10: 1461268249
• Artikelnr.: 40772718

Autorenporträt

The book is aimed particularly at students and researchers who do not have the traditional prerequisites (for example, real analysis) for a first course in functional analysis, and are interested in the applications of this subject to areas such as partial differential equations and the finite element method. The selection, presentation and organization of material are guided by the principle that abstract concepts should be conveyed in a carefully structured and well-placed manner, in order to make these readily accessible to the target readership.

Inhaltsangabe

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.