LEADER 06391nam 2200685 a 450 001 9910133589203321 005 20200520144314.0 010 $a1-280-76731-6 010 $a9786613678089 010 $a0-470-90652-9 010 $a0-470-90653-7 035 $a(CKB)3400000000000279 035 $a(EBL)675027 035 $a(OCoLC)711779377 035 $a(SSID)ssj0000477782 035 $a(PQKBManifestationID)12131099 035 $a(PQKBTitleCode)TC0000477782 035 $a(PQKBWorkID)10512739 035 $a(PQKB)11114713 035 $a(MiAaPQ)EBC675027 035 $a(PPN)169569586 035 $a(EXLCZ)993400000000000279 100 $a20100604d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGreen's functions and boundary value problems /$fIvar Stakgold, Michael J. Holst 205 $a3rd ed. 210 $aHoboken, N.J. $cWiley$d2011 215 $a1 online resource (883 p.) 225 0 $aPure and applied mathematics ;$v99 300 $aDescription based upon print version of record. 311 $a0-470-60970-2 320 $aIncludes bibliographical references and index. 327 $aGreen's Functions and Boundary Value Problems; CONTENTS; 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 327 $a2.1 Basic Ideas, Definitions, and Examples2.2 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. Hubert and Banach Spaces; 4.1 Functions and Transformations; 4.2 Linear Spaces 327 $a4.3 Metric Spaces, Normed Linear Spaces, and Banach Spaces4.4 Contractions and the Banach Fixed-Point Theorem; 4.5 Hubert Spaces and the Projection Theorem; 4.6 Separable Hubert 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 327 $a5.9 The Banach-Schauder and Banach-Steinhaus Theorems6. 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; 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 327 $a8.2 Well-Posed Problems for Hyperbolic and Parabolic Equations8.3 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 327 $a10.4 Applications to Nonlinear Elliptic Equations 330 $a"This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations. Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems. The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated"--$cProvided by publisher. 410 0$aPure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts 606 $aBoundary value problems 606 $aGreen's functions 606 $aMathematical physics 615 0$aBoundary value problems. 615 0$aGreen's functions. 615 0$aMathematical physics. 676 $a515/.35 700 $aStakgold$b Ivar$044702 701 $aHolst$b Michael J$0521857 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910133589203321 996 $aGreen's functions and boundary value problems$92001400 997 $aUNINA