一阶线性常系数微分方程组初值问题的留数解法

通过拉普拉斯变换，把一阶线性常系数微分方程组化为代数方程组，再求出代数方程组的解，此代数方程组的解是含有孤立奇点的复变函数，这些孤立奇点实际上是系数矩阵的特征根。对代数方程组的解与指数函数的乘积施行拉普拉斯逆变换，就得到原微分方程组的解。

Residue Solution to Initial Value Problems of First Order LinearConstant Coefficient Differential Equations

By Laplasse transform, first order linear constant coefficient differential equations are transformed into algebraic equations, and the solutions to the algebraic equations are found out. The solutions of the algebraic equations are complex functions with isolated singularities, and these isolated singularities are actually the characteristic roots of coefficient matrix. By performing inverse Laplasse transformation on the solutions of algebraic equations and the product of exponential function, obtains the solutions of the original differential equations.