几个典型的数学物理方程的物理解读  

Physical Interpretation of Several Typical Mathematical Physics Equations

作　　者：徐美[1] 

机构地区：[1]北京科技大学数理学院应用物理系

出　　处：《物理通报》2017年第6期33-35,39,共4页Physics Bulletin

基　　金：北京科技大学青年教学骨干人才培养计划;北京科技大学2015年度教育教学改革与研究项目,项目编号:JG2015Z02,JG2015M30

摘　　要：拉普拉斯方程、泊松方程、热传导方程（扩散方程）和波动方程是大学物理教学中常见的几个典型的微分方程,分别涉及到了流体力学、电磁学、热学和波动等重点教学内容.探索了如何用直观明确而容易理解的物理语言解读这些方程.从拉普拉斯方程的物理本质出发,通过改变该方程右端的形式,分别引出泊松方程、热传导方程（扩散方程）和波动方程,详细阐述了上述方程与相关物理现象之间的内在联系,提出了一种关于以上方程的纵向对比讲授法,为学生深入理解典型的数学物理微分方程的物理含义提供了可行的思路.Laplace＇s equation, Poisson equation, diffusion equation （heat conduction equation） and wave equation are some of the most common and typical equations in college physics teaching, which are involved in the teaching key points such as hydromechanics, electromagnetism, thermologyand undulatory theory. In this paper, we explore how to understand the aforementioned mathematical physics equationsusing clear and easy physical language. At first, the physical nature of Laplace＇s equation is explained and then Poisson equation, diffusion equation （heat conduction equation） and wave equation are introduced by changing the right side of Laplace＇s equation. The intrinsic connection between these equations and the relevant physical phenomena is described in detail. Students can understand the physical meaning of the typical mathematical physics differential equations more deeply by this longitudinal comparative teaching method for above equations.

关 键 词：数学物理方程 拉普拉斯方程 二阶偏导数 极值 

分 类 号：O175.24[理学—数学]