变分法在大学物理问题中的应用

Application of Variational Method in College Physics

摘要: 物理学中有很多问题都和极值问题有关，这些问题往往困扰着学生对普通物理的学习。处理极值问题的一个有效方法是变分方法，也就是求解一个泛函的极值问题。本文利用变分方法对几类大学物理中的极值问题进行探讨求解，归纳和总结，一方面提高学生的物理解题能力，另一方面也能增强大学生对物理问题本质的理解以及数学方法的应用。

Abstract: Many physical problems relate to extreme value problem. These problems bring troubles to many students’ study for ordinary physics. A sufficient method to deal extreme value problem is variational method that is to find extreme value for a functional. In this paper, the variational method is used to discuss the extreme value problems in several types of college physics, so as to enhance students’ understanding and solving of physical problems and the application of mathematical methods.