Guenther, Ronald B.,
Sturm-Liouville problems : theory and numerical implementation / Ronald B. Guenther, John W. Lee (Department of Mathematics, Oregon State University, Corvallis). - 1 online resource (xiii, 406 pages). - Monographs and research notes in mathematics .
Cover; Half Title; Title Page; Copyright Page; Contents; Preface; 1. Setting the Stage; 1.1 Euler Buckling; 1.2 Hanging Chain; 1.3 Separation of Variables; 1.4 Vibration Problems; 1.4.1 Vibrations of a String; 1.4.2 Vibrations of a Circular Membrane; 1.4.3 Spherically Symmetric Vibrations in a Ball; 1.5 Diffusion Problems; 1.5.1 Chemical Transport; 1.5.2 Heat Conduction in a Rod; 1.5.3 Heat Conduction in a Disk; 1.6 Steady State Regimes; 1.6.1 Heat Conduction in a Rectangular Plate; 1.6.2 Heat Conduction in a Circular Plate; 1.7 On Models; 1.8 Sturm-Liouville Boundary Value Problems 1.9 Calculus of Variations1.10 Green's Functions; 1.11 The Path Ahead; 1.11.1 Thread I; 1.11.2 Thread II; 1.11.3 Finding Eigenvalues and Eigenfunctions; 1.12 Intrinsic Interest of Eigenvalues; 1.13 Real Versus Complex Solutions; 2. Preliminaries; 2.1 Euclidean Spaces; 2.1.1 Real Euclidean Spaces; 2.1.2 Complex Euclidean Spaces; 2.1.3 Elements of Convergence; 2.1.4 Upper Bounds and Sups; 2.1.5 Closed and Compact Sets; 2.2 Calculus and Analysis; 2.2.1 Continuity; 2.2.2 Differential Calculus; 2.2.3 Integral Calculus; 2.2.4 Sequences and Series of Functions; 2.3 Matrix and Linear Algebra 2.3.1 Determinants2.3.2 Systems of Linear Algebraic Equations; 2.3.3 Linear Dependence and Linear Independence; 2.3.4 Eigenvalues and Eigenvectors; 2.3.5 Self-Adjoint and Symmetric Matrices; 2.3.6 Principal Axis Theorem; 2.3.7 Matrices as Linear Transformations; 2.4 Interpolation and Approximation; 2.4.1 Tchebycheff Systems; 2.4.2 Total Positivity; 2.5 Linear Spaces and Function Spaces; 2.5.1 Linear Spaces; 2.5.2 Normed Linear Spaces; 2.5.3 Inner Product Spaces; 2.5.3.1 Gram-Schmidt Process; 2.6 Completeness and Completion; 2.7 Compact Sets in C[a, b]; 2.8 Contraction Mapping Theorem 2.9 Bisection and Newton-Raphson Methods2.9.1 Bisection Method; 2.9.2 Newton-Raphson Method; 2.10 Maximum Principle; 3. Integral Equations; 3.1 Integral Operators; 3.2 More General Domains; 3.3 Eigenvalues of Operators and Kernels; 3.4 Self-Adjoint Operators and Kernels; 3.4.1 Hilbert-Schmidt Theorem; 3.4.2 Mercer's Theorem; 3.5 Nonnegative Kernels; 3.5.1 Positive Kernels; 3.5.2 Kernels Positive on the Open Diagonal; 3.5.3 Summary of Results; 3.6 Kellogg Kernels and Total Positivity; 3.6.1 Compound Kernels; 3.6.2 Spectral Properties of Compound Kernels 3.6.3 Spectral Properties of Kellogg Kernels3.7 Singular Kellogg Kernels; 3.7.1 Compound Kernels; 3.7.2 Spectral Properties of Compound Kernels; 3.7.3 Spectral Properties of Kellogg Kernels; 4. Regular Sturm-Liouville Problems; 4.1 Sturm-Liouville Form; 4.2 Sturm-Liouville Differential Equations; 4.3 Initial Value Problems; 4.3.1 Basis of Solutions; 4.3.2 Variation of Parameters; 4.3.3 Continuous Dependence; 4.4 BVPs and EVPs -- Examples; 4.5 BVPs and EVPs -- Notation; 4.6 Green's Functions; 4.6.1 Separated Boundary Conditions; 4.6.2 Mixed Boundary Conditions; 4.7 Adjoint Operators and Problems
Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.
9780429437878 0429437870 9780429795343 0429795343 9780429795350 0429795351 9780429795336 0429795335
Sturm-Liouville equation.
Differential equations.
Eigenvalues.
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
MATHEMATICS / Applied
MATHEMATICS / Differential Equations
MATHEMATICS / Geometry / General
QA372 / .G84 2019
515/.352
Sturm-Liouville problems : theory and numerical implementation / Ronald B. Guenther, John W. Lee (Department of Mathematics, Oregon State University, Corvallis). - 1 online resource (xiii, 406 pages). - Monographs and research notes in mathematics .
Cover; Half Title; Title Page; Copyright Page; Contents; Preface; 1. Setting the Stage; 1.1 Euler Buckling; 1.2 Hanging Chain; 1.3 Separation of Variables; 1.4 Vibration Problems; 1.4.1 Vibrations of a String; 1.4.2 Vibrations of a Circular Membrane; 1.4.3 Spherically Symmetric Vibrations in a Ball; 1.5 Diffusion Problems; 1.5.1 Chemical Transport; 1.5.2 Heat Conduction in a Rod; 1.5.3 Heat Conduction in a Disk; 1.6 Steady State Regimes; 1.6.1 Heat Conduction in a Rectangular Plate; 1.6.2 Heat Conduction in a Circular Plate; 1.7 On Models; 1.8 Sturm-Liouville Boundary Value Problems 1.9 Calculus of Variations1.10 Green's Functions; 1.11 The Path Ahead; 1.11.1 Thread I; 1.11.2 Thread II; 1.11.3 Finding Eigenvalues and Eigenfunctions; 1.12 Intrinsic Interest of Eigenvalues; 1.13 Real Versus Complex Solutions; 2. Preliminaries; 2.1 Euclidean Spaces; 2.1.1 Real Euclidean Spaces; 2.1.2 Complex Euclidean Spaces; 2.1.3 Elements of Convergence; 2.1.4 Upper Bounds and Sups; 2.1.5 Closed and Compact Sets; 2.2 Calculus and Analysis; 2.2.1 Continuity; 2.2.2 Differential Calculus; 2.2.3 Integral Calculus; 2.2.4 Sequences and Series of Functions; 2.3 Matrix and Linear Algebra 2.3.1 Determinants2.3.2 Systems of Linear Algebraic Equations; 2.3.3 Linear Dependence and Linear Independence; 2.3.4 Eigenvalues and Eigenvectors; 2.3.5 Self-Adjoint and Symmetric Matrices; 2.3.6 Principal Axis Theorem; 2.3.7 Matrices as Linear Transformations; 2.4 Interpolation and Approximation; 2.4.1 Tchebycheff Systems; 2.4.2 Total Positivity; 2.5 Linear Spaces and Function Spaces; 2.5.1 Linear Spaces; 2.5.2 Normed Linear Spaces; 2.5.3 Inner Product Spaces; 2.5.3.1 Gram-Schmidt Process; 2.6 Completeness and Completion; 2.7 Compact Sets in C[a, b]; 2.8 Contraction Mapping Theorem 2.9 Bisection and Newton-Raphson Methods2.9.1 Bisection Method; 2.9.2 Newton-Raphson Method; 2.10 Maximum Principle; 3. Integral Equations; 3.1 Integral Operators; 3.2 More General Domains; 3.3 Eigenvalues of Operators and Kernels; 3.4 Self-Adjoint Operators and Kernels; 3.4.1 Hilbert-Schmidt Theorem; 3.4.2 Mercer's Theorem; 3.5 Nonnegative Kernels; 3.5.1 Positive Kernels; 3.5.2 Kernels Positive on the Open Diagonal; 3.5.3 Summary of Results; 3.6 Kellogg Kernels and Total Positivity; 3.6.1 Compound Kernels; 3.6.2 Spectral Properties of Compound Kernels 3.6.3 Spectral Properties of Kellogg Kernels3.7 Singular Kellogg Kernels; 3.7.1 Compound Kernels; 3.7.2 Spectral Properties of Compound Kernels; 3.7.3 Spectral Properties of Kellogg Kernels; 4. Regular Sturm-Liouville Problems; 4.1 Sturm-Liouville Form; 4.2 Sturm-Liouville Differential Equations; 4.3 Initial Value Problems; 4.3.1 Basis of Solutions; 4.3.2 Variation of Parameters; 4.3.3 Continuous Dependence; 4.4 BVPs and EVPs -- Examples; 4.5 BVPs and EVPs -- Notation; 4.6 Green's Functions; 4.6.1 Separated Boundary Conditions; 4.6.2 Mixed Boundary Conditions; 4.7 Adjoint Operators and Problems
Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.
9780429437878 0429437870 9780429795343 0429795343 9780429795350 0429795351 9780429795336 0429795335
Sturm-Liouville equation.
Differential equations.
Eigenvalues.
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
MATHEMATICS / Applied
MATHEMATICS / Differential Equations
MATHEMATICS / Geometry / General
QA372 / .G84 2019
515/.352