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Green's functions and boundary value problems / Ivar Stakgold, Michael Holst.

By: Contributor(s): Material type: TextTextSeries: Pure and applied mathematics (John Wiley & Sons : Unnumbered)Publication details: Hoboken, N.J. : Wiley, ©2011.Edition: 3rd edDescription: 1 online resource (xxi, 855 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780470906538
  • 0470906537
  • 9780470906521
  • 0470906529
Subject(s): Genre/Form: Additional physical formats: Print version:: Green's functions and boundary value problems.DDC classification:
  • 515/.35 22
LOC classification:
  • QA379 .S72 2011
Online resources:
Contents:
Green's functions (intuitive ideas) -- The theory of distributions -- One-dimensional boundary value problems -- Hilbert and Banach spaces -- Operator theory -- Integral equations -- Spectral theory of second-order differential operators -- Partial differential equations -- Nonlinear problems -- Approximation theory and methods.
Summary: "This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated"--Provided by publisher.
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"This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated"--Provided by publisher.

Includes bibliographical references and index.

Green's functions (intuitive ideas) -- The theory of distributions -- One-dimensional boundary value problems -- Hilbert and Banach spaces -- Operator theory -- Integral equations -- Spectral theory of second-order differential operators -- Partial differential equations -- Nonlinear problems -- Approximation theory and methods.

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