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Introductory Functional Analysis

With Applications to Boundary Value Problems and Finite Elements

  • Textbook
  • © 1998

Overview

Authors:
  1. B. Daya Reddy

    1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa

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  • Assumes only elementary knowledge of linear algebra, vector analysis, and differential equations
  • New concepts made more accessible by copious use of concrete worked examples
  • Descriptive approach favored over detailed mathematical argument
  • Chapter end with exercises to consolidate the material
  • Solutions included

Part of the book series: Texts in Applied Mathematics (TAM, volume 27)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    1. Introduction

      • B. Daya Reddy
      Pages 1-19

  3. Linear Functional Analysis

    1. Front Matter

      Pages 21-21
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    2. Sets

      • B. Daya Reddy
      Pages 23-51

    3. Sets of functions and Lebesgue integration

      • B. Daya Reddy
      Pages 53-80

    4. Vector spaces, normed, and inner product spaces

      • B. Daya Reddy
      Pages 81-104

    5. Properties of normed spaces

      • B. Daya Reddy
      Pages 105-131

    6. Linear operators

      • B. Daya Reddy
      Pages 133-174

    7. Orthonormal bases and Fourier series

      • B. Daya Reddy
      Pages 175-212

    8. Distributions and Sobolev spaces

      • B. Daya Reddy
      Pages 213-251

  4. Elliptic Boundary Value Problems

    1. Front Matter

      Pages 253-253
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    2. Elliptic boundary value problems

      • B. Daya Reddy
      Pages 255-303

    3. Variational boundary value problems

      • B. Daya Reddy
      Pages 305-338

    4. Approximate methods of solution

      • B. Daya Reddy
      Pages 339-359

  5. The Finite Element Method

    1. Front Matter

      Pages 361-361
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    2. The finite element method

      • B. Daya Reddy
      Pages 363-409

    3. Analysis of the finite element method

      • B. Daya Reddy
      Pages 411-434

  6. Back Matter

    Pages 435-471
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, South Africa

    B. Daya Reddy

Bibliographic Information

  • Book Title: Introductory Functional Analysis

  • Book Subtitle: With Applications to Boundary Value Problems and Finite Elements

  • Authors: B. Daya Reddy

  • Series Title: Texts in Applied Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0575-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98307-3Published: 20 November 1997

  • Softcover ISBN: 978-1-4612-6824-6Published: 20 November 2013

  • eBook ISBN: 978-1-4612-0575-3Published: 27 November 2013

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 1

  • Number of Pages: XIV, 472

  • Topics: Analysis, Computational Intelligence, Theoretical, Mathematical and Computational Physics

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