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: Applied Pseudoanalytic Function Theory
  name:
    name part: Kravchenko, Vladislav V.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 184 p. online resource.
  abstract: Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.
  table of contents: Pseudoanalytic Function Theory and Second-order Elliptic Equations -- Definitions and Results from Bers’ Theory -- Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions -- Formal Powers -- Cauchy’s Integral Formula -- Complex Riccati Equation -- Applications to Sturm-Liouville Theory -- A Representation for Solutions of the Sturm-Liouville Equation -- Spectral Problems and Darboux Transformation -- Applications to Real First-order Systems -- Beltrami Fields -- Static Maxwell System in Axially Symmetric Inhomogeneous Media -- Hyperbolic Pseudoanalytic Functions -- Hyperbolic Numbers and Analytic Functions -- Hyperbolic Pseudoanalytic Functions -- Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation -- Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications -- The Dirac Equation -- Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions -- Multidimensional Second-order Equations.
  note: by Vladislav V. Kravchenko.
  subject:
    topic: Mathematics
  subject:
    topic: Functions of complex variables
  subject:
    topic: Operator theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Operator Theory
  subject:
    topic: Functions of a Complex Variable
  subject:
    topic: Several Complex Variables and Analytic Spaces
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Frontiers in Mathematics
  identifier: 9783034600040
  identifier: http://dx.doi.org/10.1007/978-3-0346-0004-0
  record info:
    record creation date: 100301
    record change date: 20151125151508.0
    record identifier: 978-3-0346-0004-0