rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Implicit Functions and Solution Mappings
    sub title: A View from Variational Analysis
  name:
    name part: Dontchev, Asen L.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Rockafellar, R. Tyrrell.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2014
    edition: 2nd ed. 2014.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVIII, 466 p. 14 illus., 1 illus. in color. online resource.
  abstract: The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section. From reviews of the first edition: “The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide, and a somewhat brief index complete this study. … I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.” (Jonathan Michael Borwein, IEEE Control Systems Magazine, February, 2012) “This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. … The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics, and so on.” (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010) “The …
  table of contents: Introduction and equation-solving background -- Solution mappings for variational problems -- Set-valued analysis of solution mappings -- Regularity properties through generalized derivatives -- Metric regularity in infinite dimensions -- Applications in numerical variational analysis.
  note: by Asen L. Dontchev, R. Tyrrell Rockafellar.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematical optimization
  subject:
    topic: Mathematics
  subject:
    topic: Optimization
  subject:
    topic: Analysis
  subject:
    topic: Numerical Analysis
  classification: QA402.5-402.6
  classification: 519.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Series in Operations Research and Financial Engineering
  identifier: 9781493910373
  identifier: http://dx.doi.org/10.1007/978-1-4939-1037-3
  record info:
    record creation date: 140618
    record change date: 20151030061404.0
    record identifier: 978-1-4939-1037-3