留数在有理分式拉普拉斯反演中的应用

The Application of Residue in Rational Fraction Inversion in Laplace

有理分式的拉普拉斯反演的教学难点就是分项分式的求解。基于教学中有理分式函数分解为几个有理真分式函数之和时系数的确定,文中结合Cauchy定理和留数的概念,提出一种求待定系数的新方法——留数法。以教学实例,说明留数法较比较法和赋值法求待定系数简单,也容易被学生理解和掌握。

The difficulty of the Laplace inversion of rational fraction is the solution of the partial fraction. Based on the determination of coeffi cient when the rational function is decomposed into some rational fractional function in teaching and combining the residue concept and the Cauchy theorem, a new method is proposed for undetermined coefficient-residue method. In teaching practice, compared with comparison and assignment method for the undetermined coeffi cient, the residue method is simple to use and also easy for students to understand and master.