作者：王桂霞,玉林
页数：144
出版社：厦门大学出版社
出版日期：2023
ISBN：9787561591864
电子书格式：pdf/epub/txt
内容简介
全书使用泛函分析、算子代数、微分方程、不等式估计分析、数值计算等多学科领域的思想方法和技术手段，对 Sturm-Liouville 算子中基本且重要问题进行了研究和探讨，主要内容包括非连续Sturm-Liouville 算子理论、Sturm-Liouville 边值问题的数值求解方法以及非连续Sturm-Liouville 边值问题在海洋内波中的应用研究。本书可作为计算数学和应用数学高年级本科生和研究生的选修课教材，也可供相关领域工作的教师和科研人员阅读参考。
本书特色
全书使用泛函分析、算子代数、微分方程、不等式估计分析、数值计算等多学科领域的思想方法和技术手段，对 Sturm-Liouville 算子中基本且重要问题进行了研究和探讨，主要内容包括非连续Sturm-Liouville 算子理论、Sturm-Liouville 边值问题的数值求解方法以及非连续Sturm-Liouville 边值问题在海洋内波中的应用研究。本书可作为计算数学和应用数学高年级本科生和研究生的选修课教材，也可供相关领域工作的教师和科研人员阅读参考。
目录
Chapter 1 Introduction
1.1 Physical background
1.2 Related results of ordinary differential operators
1.3 Structure of the book
Chapter 2 Approximations of eigenvalues and eigenfunctions
2.1 Notation and theoretic results
2.2 Main ideas of the algorithms
2.3 General methods for constructing examples
2.4 Examples with 2-independent BCs
2.5 Examples with 2-dependent BCs
2.6 Oscillations of eigenfunctions for discontinuous Sturm-Liouville problems
Chapter 3 Computing the indices of eigenvalues
3.1 Notation and theoretic results
3.2 Algorithm and implementation
3.3 Examples with a positive f
3.4 Examples with an indefinite f
3.5 Examples about β最(α) and β(α)
Chapter 4 Relations among eigenvalues of Sturm-Liouville problems
4.1 Notation and basic results
4.2 Geometric characterization of λn
4.3 Interlacing relations among eigenvalues
Chapter 5 Third-order eigenparameter dependent differential operators
5.1 Preliminaries
5.2 The Banach space
5.3 Derivative formulas of eigenvalues
Chapter 6 Application of Sturm-Liouville problems
6.1 Construction and stability of Riesz bases
6.2 Eigenvalue problems of internal solitary waves
Appendix A Fundamentals Sturm-Liouville problems
A.1 Classes of Sturm-Liouville problems
A.2 Characteristic function
Appendix B Thomson-Haskell method
Appendix C First-order linear differential equations
C.1 Existence and uniqueness of a solution
C.2 Rank of a solution and variation of parameters
C.3 Continuous dependence of solution on the problem
References
1.1 Physical background
1.2 Related results of ordinary differential operators
1.3 Structure of the book
Chapter 2 Approximations of eigenvalues and eigenfunctions
2.1 Notation and theoretic results
2.2 Main ideas of the algorithms
2.3 General methods for constructing examples
2.4 Examples with 2-independent BCs
2.5 Examples with 2-dependent BCs
2.6 Oscillations of eigenfunctions for discontinuous Sturm-Liouville problems
Chapter 3 Computing the indices of eigenvalues
3.1 Notation and theoretic results
3.2 Algorithm and implementation
3.3 Examples with a positive f
3.4 Examples with an indefinite f
3.5 Examples about β最(α) and β(α)
Chapter 4 Relations among eigenvalues of Sturm-Liouville problems
4.1 Notation and basic results
4.2 Geometric characterization of λn
4.3 Interlacing relations among eigenvalues
Chapter 5 Third-order eigenparameter dependent differential operators
5.1 Preliminaries
5.2 The Banach space
5.3 Derivative formulas of eigenvalues
Chapter 6 Application of Sturm-Liouville problems
6.1 Construction and stability of Riesz bases
6.2 Eigenvalue problems of internal solitary waves
Appendix A Fundamentals Sturm-Liouville problems
A.1 Classes of Sturm-Liouville problems
A.2 Characteristic function
Appendix B Thomson-Haskell method
Appendix C First-order linear differential equations
C.1 Existence and uniqueness of a solution
C.2 Rank of a solution and variation of parameters
C.3 Continuous dependence of solution on the problem
References
