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:
    non sort: The
    title: Implicit Function Theorem
    sub title: History, Theory, and Applications
  name:
    name part: Krantz, Steven G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Parks, Harold R.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 163 p. online resource.
  abstract: The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash–Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph. Originally published in 2002, The Implicit Function Theorem is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.
  table of contents: Preface -- Introduction to the Implicit Function Theorem -- History -- Basic Ideas -- Applications -- Variations and Generalizations -- Advanced Implicit Function Theorems -- Glossary -- Bibliography -- Index.
  note: by Steven G. Krantz, Harold R. Parks.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Differential equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Differential geometry
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Differential Geometry
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Ordinary Differential Equations
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Modern Birkhäuser Classics
  identifier: 9781461459811
  identifier: http://dx.doi.org/10.1007/978-1-4614-5981-1
  record info:
    record creation date: 121116
    record change date: 20151125192512.0
    record identifier: 978-1-4614-5981-1