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Full but Elementary Treatment of Systems of Homogeneous Ordinary Linear Differential Equations with Constant Coefficients

机译：常系数齐次线性微分方程组的全基本处理

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摘要

To discuss completely how to construct the general solution of homogeneous linear differential equations with constant coefficients is not simple. Indeed, in many textbooks it is said to be beyond the scope of the book; or concepts from linear algebra such as direct sum, generalized eigenspace, Jordan canonical form, are taken for granted. In the paper it is shown that one needs only the most elementary results from linear algebra to give a full treatment. Also it is shown that Fulmer's method for calculating the fundamental solution can be proved without assuming the Cayley-Hamilton theorem from linear algebra.

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作者
Besjes, J. G.;
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年度 1987
页码 p.1-14
总页数 14
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Linear differential equations ; Ordinary differential equations ; Matrices(Mathematics);

机译：线性微分方程;常微分方程;矩阵（数学）;

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专利

1. A general technique for converting n x n systems of linear ordinary differential equations with constant coefficients to a single high order equation [J] . W. Robin Nonlinear Analysis and Differential Equations . 2014,第4期

机译：将具有常数系数的n x n个线性常微分方程组转换为单个高阶方程的通用技术
2. A METHOD FOR THE DISCRETIZATION OF LINEAR SYSTEMS OF ORDINARY FRACTIONAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [J] . F. A. Aliev, N. A. Aliev, N. I. Velieva, Journal of Mathematical Sciences . 2021,第5期

机译：恒定系数的普通分数微分方程线性系统离散化方法
3. Algorithm 982: Explicit Solutions of Triangular Systems of First-Order Linear Initial-Value Ordinary Differential Equations with Constant Coefficients [J] . Van Snyder W. ACM transactions on mathematical software . 2017,第2期

机译：算法982：具有常数系数的一阶线性初值常微分方程的三角系统的显式解
4. Analytical matrix solutions of linear ordinary differential equations with constant coefficients [C] . Y I Vinogradov, D B Molchanov, V N Bakulin International Conference "Supercomputer Technologies of Mathematical Modelling" . 2020

机译：恒定系数线性常微分方程的分析矩阵解
5. Applications of Nonlinear Systems of Ordinary Differential Equations and Volterra Integral Equations to Infectious Disease Epidemiology. [D] . Morale Butler, Emmanuel J. 2014

机译：常微分方程和Volterra积分方程的非线性系统在传染病流行病学中的应用。
6. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients [O] . Vyacheslav M. Boyko, Roman O. Popovych, Nataliya M. Shapoval -1

机译：常系数二阶线性常微分方程组的Lie对称性
7. On linear and nonlinear perturbations of linear systems of ordinary differential equations with constant coefficients [O] . Philip Hartman, Aurel Wintner 1956

机译：恒定系数的常微分方程线性系统的线性和非线性扰动
8. Expansions in Series of Homogeneous Polynomial Solutions of the General Two-Dimensional Linear Partial Differential Equation of the Second Order with Constant Coefficients [R] . D. V. Widder 1958

机译：常系数二阶一般二维线性偏微分方程齐次多项式解的一系列展开式

Full but Elementary Treatment of Systems of Homogeneous Ordinary Linear Differential Equations with Constant Coefficients

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