And knowing now how to calculate these free energies especially the Helmholtz and the Gibbs free energies,that's what's going to guide us in really calculating quantitatively, OK, where will equilibrium lie.

知道如何计算,这些自由能,尤其是亥姆赫兹和吉布斯自由能之后,这些数值计算就能告诉我们，平衡态到底是什么样子。

麻省理工公开课 - 热力学与动力学课程节选

There're also changes of what you can teach, extends what you can teach, because you can get to concept which are really quite sophisticated that you will never teach it at the introductory level, because the math is the least that you can make it quantitatively, because you have a visualization that shows physically what's going on.

同时这也能改变,教学内容，你能教授的程度，因为你可以定义,那些通常很难的,你在入门阶段都不会遇到的,抽象阶段，因为数学是你最不能,用定量手段来解决的，因为你有一个直观过程,知道什么正在进行。

麻省理工公开课 - 媒体、教育、市场课程节选