Green's functions and linear differential equations : theory, applications and computation /: theory, applications and computation. (2015)

• Record Type: Book
• Further Information: Note: Prem K. Kythe.
• Authors: Kythe, Prem K
• Contents: Some Basic Results; Euclidean Space; Classes of Continuous Functions; Convergence; Functionals; Linear Transformations; Cramer’s Rule; Green’s Identities; Differentiation and Integration; Inequalities The Concept of Green’s Functions; Generalized Functions; Singular Distributions; The Concept of Green’s Functions; Linear Operators and Inverse Operators; Fundamental Solutions Sturm–Liouville Systems; Ordinary Differential Equations; Initial Value Problems; Boundary Value Problems; Eigenvalue Problem for Sturm–Liouville Systems; Periodic Sturm–Liouville Systems; Singular Sturm–Liouville Systems Bernoulli’s Separation Method; Coordinate Systems; Partial Differential Equations; Bernoulli’s Separation Method; Examples Integral Transforms; Integral Transform Pairs ; Laplace Transform; Fourier Integral Theorems; Fourier Sine and Cosine Transforms; Finite Fourier Transforms; Multiple Transforms; Hankel Transforms; Summary: Variables of Transforms Parabolic Equations; 1-D Diffusion Equation; 2-D Diffusion Equation; 3-D Diffusion Equation; Schrödinger Diffusion Operator; Min-Max Principle; Diffusion Equation in a Finite Medium; Axisymmetric Diffusion Equation; 1-D Heat Conduction Problem; Stefan Problem; 1-D Fractional Diffusion Equation; 1-D Fractional Schrödinger Diffusion Equation; Eigenpairs and Dirac Delta Function Hyperbolic Equations; 1-D Wave Equation; 2-D Wave Equation; 3-D Wave Equation; 2-D Axisymmetric Wave Equation; Vibrations of a Circular Membrane; 3-D Wave Equation in a Cube; Schrödinger Wave Equation; Hydrogen Atom; 1-D Fractional Nonhomogeneous Wave Equation; Applications of the Wave Operator; Laplace Transform Method; Quasioptics and Diffraction Elliptic Equations; Green’s Function for 2-D Laplace’s Equation; 2-D Laplace’s Equation in a Rectangle; Green’s Function for 3-D Laplace’s Equation; Harmonic Functions; 2-D Helmholtz’s Equation; Green’s Function for 3-D Helmholtz’s Equation; 2-D Poisson’s Equation in a Circle; Method for Green’s Function in a Rectangle; Poisson’s Equation in a Cube; Laplace’s Equation in a Sphere; Poisson’s Equation and Green’s Function in a Sphere; Applications of Elliptic Equations Spherical Harmonics; Historical Sketch; Laplace’s Solid Spherical Harmonics; Surface Spherical Harmonics Conformal Mapping Method; Definitions and Theorems; Dirichlet Problem; Neumann Problem; Green’s and Neumann’s Functions; Computation of Green’s Functions Appendix A: Adjoint Operators ; Appendix B: List of Fundamental Solutions; Appendix C: List of Spherical Harmonics ; Appendix D: Tables of Integral Transforms ; Appendix E: Fractional Derivatives ; Appendix F: Systems of Ordinary Differential Equations Bibliography Index Exercises appear at the end of each chapter, with hints, answers, and, sometimes, complete solutions.
• Publisher Details: Boca Raton, Florida : CRC Press
• Publication Date: 2015
• Copyright Date: 2015
• Extent: 1 online resource (376 pages)
• Subjects: 515.353; Differential equations, Partial; Green's functions; Differential equations, Partial; Green's functions; Electronic books
• Languages: English
• ISBNs: 9781439840092; 1439840091
• Related ISBNs: 9781439840085
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (ebrary, viewed January 20, 2015).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.