Green's Functions and Boundary Value Problems / Wiley Series in Pure and Applied Mathematics (PDF)
(Sprache: Englisch)
Praise for the Second Edition
"This book is an excellent introduction to the wide field of
boundary value problems."--Journal of Engineering
Mathematics
"No doubt this textbook will be useful for both students and
research...
"This book is an excellent introduction to the wide field of
boundary value problems."--Journal of Engineering
Mathematics
"No doubt this textbook will be useful for both students and
research...
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Praise for the Second Edition
"This book is an excellent introduction to the wide field of
boundary value problems."--Journal of Engineering
Mathematics
"No doubt this textbook will be useful for both students and
research workers."--Mathematical Reviews
A new edition of the highly-acclaimed guide to boundary value
problems, now featuring modern computational methods and
approximation theory
Green's Functions and Boundary Value Problems, Third Edition
continues the tradition of the two prior editions by providing
mathematical techniques for the use of differential and integral
equations to tackle important problems in applied mathematics, the
physical sciences, and engineering. This new edition presents
mathematical concepts and quantitative tools that are essential for
effective use of modern computational methods that play a key role
in the practical solution of boundary value problems. With a
careful blend of theory and applications, the authors successfully
bridge the gap between real analysis, functional analysis,
nonlinear analysis, nonlinear partial differential equations,
integral equations, approximation theory, and numerical analysis to
provide a comprehensive foundation for understanding and analyzing
core mathematical and computational modeling problems.
Thoroughly updated and revised to reflect recent developments,
the book includes an extensive new chapter on the modern tools of
computational mathematics for boundary value problems. The Third
Edition features numerous new topics, including:
* Nonlinear analysis tools for Banach spaces
* Finite element and related discretizations
* Best and near-best approximation in Banach spaces
* Iterative methods for discretized equations
* Overview of Sobolev and Besov space linear
* Methods for nonlinear equations
* Applications to nonlinear elliptic equations
In addition, various topics have been substantially expanded,
and new material on weak derivatives and Sobolev spaces, the
Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder
and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been
incorporated into the book. New and revised exercises found
throughout allow readers to develop their own problem-solving
skills, and the updated bibliographies in each chapter provide an
extensive resource for new and emerging research and
applications.
With its careful balance of mathematics and meaningful
applications, Green's Functions and Boundary Value Problems, Third
Edition is an excellent book for courses on applied analysis and
boundary value problems in partial differential equations at the
graduate level. It is also a valuable reference for mathematicians,
physicists, engineers, and scientists who use applied mathematics
in their everyday work.
"This book is an excellent introduction to the wide field of
boundary value problems."--Journal of Engineering
Mathematics
"No doubt this textbook will be useful for both students and
research workers."--Mathematical Reviews
A new edition of the highly-acclaimed guide to boundary value
problems, now featuring modern computational methods and
approximation theory
Green's Functions and Boundary Value Problems, Third Edition
continues the tradition of the two prior editions by providing
mathematical techniques for the use of differential and integral
equations to tackle important problems in applied mathematics, the
physical sciences, and engineering. This new edition presents
mathematical concepts and quantitative tools that are essential for
effective use of modern computational methods that play a key role
in the practical solution of boundary value problems. With a
careful blend of theory and applications, the authors successfully
bridge the gap between real analysis, functional analysis,
nonlinear analysis, nonlinear partial differential equations,
integral equations, approximation theory, and numerical analysis to
provide a comprehensive foundation for understanding and analyzing
core mathematical and computational modeling problems.
Thoroughly updated and revised to reflect recent developments,
the book includes an extensive new chapter on the modern tools of
computational mathematics for boundary value problems. The Third
Edition features numerous new topics, including:
* Nonlinear analysis tools for Banach spaces
* Finite element and related discretizations
* Best and near-best approximation in Banach spaces
* Iterative methods for discretized equations
* Overview of Sobolev and Besov space linear
* Methods for nonlinear equations
* Applications to nonlinear elliptic equations
In addition, various topics have been substantially expanded,
and new material on weak derivatives and Sobolev spaces, the
Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder
and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been
incorporated into the book. New and revised exercises found
throughout allow readers to develop their own problem-solving
skills, and the updated bibliographies in each chapter provide an
extensive resource for new and emerging research and
applications.
With its careful balance of mathematics and meaningful
applications, Green's Functions and Boundary Value Problems, Third
Edition is an excellent book for courses on applied analysis and
boundary value problems in partial differential equations at the
graduate level. It is also a valuable reference for mathematicians,
physicists, engineers, and scientists who use applied mathematics
in their everyday work.
Inhaltsverzeichnis zu „Green's Functions and Boundary Value Problems / Wiley Series in Pure and Applied Mathematics (PDF)“
Preface to Third Edition. Preface to Second Edition. Preface to First Edition. 0 Preliminaries. 0.1 Heat Conduction. 0.2 Diffusion. 0.3 Reaction-Diffusion Problems. 0.4 The Impulse-Momentum Law: The Motion of Rods and Strings. 0.5 Alternative Formulations of Physical Problems. 0.6 Notes on Convergence. 0.7 The Lebesgue Integral. 1 Green's Functions (Intuitive Ideas). 1.1 Introduction and General Comments. 1.2 The Finite Rod. 1.3 The Maximum Principle. 1.4 Examples of Green's Functions. 2 The Theory of Distributions. 2.1 Basic Ideas, Definitions, and Examples. 2.2 Convergence of Sequences and Series of Distributions. 2.3 Fourier Series. 2.4 Fourier Transforms and Integrals. 2.5 Differential Equations in Distributions. 2.6 Weak Derivatives and Sobolev Spaces. 3 One-Dimensional Boundary Value Problems. 3.1 Review. 3.2 Boundary Value Problems for Second-Order Equations. 3.3 Boundary Value Problems for Equations of Order p. 3.4 Alternative Theorems. 3.5 Modified Green's Functions. 4 Hilbert and Banach Spaces. 4.1 Functions and Transformations. 4.2 Linear Spaces. 4.3 Metric Spaces, Normed Linear Spaces, and Banach Spaces. 4.4 Contractions and the Banach Fixed-Point Theorem. 4.5 Hilbert Spaces and the Projection Theorem. 4.6 Separable Hilbert Spaces and Orthonormal Bases. 4.7 Linear Functionals and the Riesz Representation Theorem. 4.8 The Hahn-Banach Theorem and Reflexive Banach Spaces. 5 Operator Theory. 5.1 Basic Ideas and Examples. 5.2 Closed Operators. 5.3 Invertibility: The State of an Operator. 5.4 Adjoint Operators. 5.5 Solvability Conditions. 5.6 The Spectrum of an Operator. 5.7 Compact Operators. 5.8 Extremal Properties of Operators. 5.9 The Banach-Schauder and Banach-Steinhaus Theorems. 6 Integral Equations. 6.1 Introduction. 6.2 Fredholm Integral Equations. 6.3 The Spectrum of a Self-Adjoint Compact Operator. 6.4 The Inhomogeneous Equation. 6.5 Variational Principles and Related Approximation Methods. 7 Spectral Theory of Second-Order Differential Operators.
... mehr
7.1 Introduction; The Regular Problem. 7.2 Weyl's Classification of Singular Problems. 7.3 Spectral Problems with a Continuous Spectrum. 8 Partial Differential Equations. 8.1 Classification of Partial Differential Equations. 8.2 Well-Posed Problems for Hyperbolic and Parabolic Equations. 8.3 Elliptic Equations. 8.4 Variational Principles for Inhomogeneous Problems. 8.5 The Lax-Milgram Theorem. 9 Nonlinear Problems. 9.1 Introduction and Basic Fixed-Point Techniques. 9.2 Branching Theory. 9.3 Perturbation Theory for Linear Problems. 9.4 Techniques for Nonlinear Problems. 9.5 The Stability of the Steady State. 10 Approximation Theory and Methods. 10.1 Nonlinear Analysis Tools for Banach Spaces. 10.2 Best and Near-Best Approximation in Banach Spaces. 10.3 Overview of Sobolev and Besov Spaces. 10.4 Applications to Nonlinear Elliptic Equations. 10.5 Finite Element and Related Discretization Methods. 10.6 Iterative Methods for Discretized Linear Equations. 10.7 Methods for Nonlinear Equations. Index.
... weniger
Autoren-Porträt von Ivar Stakgold, Michael J. Holst
IVAR STAKGOLD, PhD, is Professor Emeritus and former Chairof the Department of Mathematical Sciences at the University of
Delaware. He is former president of the Society for Industrial and
Applied Mathematics (SIAM), where he was also named a SIAM Fellow
in the inaugural class of 2009. Dr. Stakgold's research interests
include nonlinear partial differential equations,
reaction-diffusion, and bifurcation theory.
MICHAEL HOLST, PhD, is Professor in the Departments of
Mathematics and Physics at the University of California, San Diego,
where he is also CoDirector of both the Center for Computational
Mathematics and the Doctoral Program in Computational Science,
Mathematics, and Engineering. Dr. Holst has published numerous
articles in the areas of applied analysis, computational
mathematics, partial differential equations, and mathematical
physics.
Bibliographische Angaben
- Autoren: Ivar Stakgold , Michael J. Holst
- 2011, 3. Auflage, 880 Seiten, Englisch
- Verlag: John Wiley & Sons
- ISBN-10: 0470906529
- ISBN-13: 9780470906521
- Erscheinungsdatum: 01.03.2011
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