分离变量法教学内容优化及本征值问题引入方式研究

The Optimizing of Teaching Content for the Separation Variables Method and Research on the Introduction Mode of the Eigenvalue Issue

现有数学物理方法教学体系中,分离变量法在前,本征值问题在后.而分离变量过程中,又涉及到本征值问题.这样的安排导致学生在学习分离变量法过程中,不能很好地理解本征值问题是分离变量法的基础,不利于学生严密逻辑思维能力的培养.针对这个问题我们开展了分离变量法教学内容优化的研究,提出一种更有利于学生严密逻辑思维能力培养的分离变量法教学方案.将本征值问题提前,将其置于定解问题之后、分离变量法之前.进而,为避免直接引入Sturm-Liouville方程而导致的突兀性问题,给出了分离变量法教学顺序调整后的Sturm-Liouville方程的引出方案.

The method of separation of variables in the first eigenvalue problem last in present teaching system of mathematical physical methods, which leads to the students are not well understand that the foundation of the method of separation of variables is eigenvalue problem,and is not conducive to develop the strict logical thinking ability. We carry out the study of op develop student＇s logical thinking abil variables, and present the introducing Sturm - Liouville equation. tim ity. ization of teaching contents,and present a more favorable solution to We introduce the eigenvalue problem before the method separation of scheme of Sturm - Liouville equation to avoiding the abrupt appearance of