论文标题
用启发式方法揭示部分微分方程的物理学
Unveiling the physics of partial differential equations with heuristics
论文作者
论文摘要
部分微分方程的启发式论点和数量级估计突出了他们描述的物理学的基本特征。我们介绍了数学物理学的三个经典二阶PDE（波，热和拉普拉斯方程），用于一阶传输方程以及两个非线性波方程的三个经典二阶PDE（波，热，热和拉普拉斯方程）的数量级估计及其局限性。在跳入更严格的数学之前，将开学生接触到这些考虑因素是有益的。然而，这些简单的论点在物理教科书中缺少。
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second order PDEs of mathematical physics (wave, heat, and Laplace equations), for first order transport equations, and for two non-linear wave equations. It is beneficial to expose the beginning student to these considerations before jumping into more rigorous mathematics. Yet these simple arguments are missing from physics textbooks.
