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所在平台: Udemy |
课程主页: https://www.udemy.com/course/mathematical-tools-for-thermodynamics-1/
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课程名称：热力学的数学工具 1 课程概述：本课程专为从未学习过热力学或未接受过高级微积分课程的学员设计。只需具备高中学历即可参与，课程内容以直接应用为主，详细解释每一个细节。每个小测验均附有详细的答案和解释。在学习热力学之前，我们需要掌握一些数学工具，如：偏导数、混合二次偏导数、微分形式、两个变量函数的积分、状态函数的概念、路径积分、积分因子等。我们将为初学者呈现所有这些概念，讲解方法涵盖从A到Z的计算过程。 课程内容及概述：课程时长约4小时，使用白板进行授课，模拟真实大学课堂，以实现沉浸式学习。我们首先回顾极坐标，然后进行一场有详细解析的小测验，接着深入偏导数概念，重点关注仅有两个变量的函数，但掌握了两个变量后，便能自然理解多个变量的情况。之后，我们将探讨混合导数。在课程中会重温一些高中时学过的导数规则。第一部分结束时，我们将介绍热力学中的一个有趣属性与普遍结果。 第二部分，我们将重点学习微分形式，这在热力学中是一个极其重要的概念，特别是精确微分形式的概念，因为热力学中所有函数的微分都是精确的。第三部分将讨论“状态函数”的概念，因为所有热力学函数都是状态函数。 最后，第四部分是对之前内容的应用总结，我们将计算非常简单的初学者路径积分，以展示这样的积分是存在的，并且可能依赖于所采用的路径。结束时，我们还将提供积分因子的示例，乘以微分形式后可以进行积分，因此得名。 希望通过本课程，帮助学习者打下坚实的热力学数学基础，从而顺利进入热力学的学习。
This course is reserved for people who have never had a thermodynamics course, or who have never had an advanced course on differential calculus. Anyone can use it just needs a HighSchool Diploma level, this course is presented as a direct application where every detail is explained. Each quiz contains a detailed answer with explanation. Before any thermodynamics course we need mathematical tools like: The partial derivativeMixed second partial derivativedifferential formintegral of function of two variablesnotion of state functionpath integralintegrating factor In this course we present all this concept for beginner Our method is detailed the calculation from A to Z. Content and Overview About 4 hours of classes using a white board as a real university course for total immersion. We start with a recall about the polar coordinates followed directly by a quiz with detailed correction, after this we attack the notion of partial derivative of a function of several variables, here, for simplicity we will only see the functions of two variables, but to understand for two variables is to understand automatically for several variables, after that, we will see the mixed derivative. During our course we will see quite a recall on some rules of derivation already seen in high school. At the end of section 1 we will see an interesting property in thermodynamics, a general result. In the second part of this course we shall attack the notion of differential forms, very important concept in thermodynamics, we shall see especially the notion of an exact differential form of a function, since all the functions in thermodynamics their differential is exact. In the third part we will see the notion of "state function", because all the thermodynamic functions are state functions. Finally part 4 is a great application of that has been seen previously, it is like a summary, but in this part we will also calculate very simple path integrals for beginners, just to see that there exist such integrals, wich may depend on the path taken. And at the end we will see an example of an integrating factor, which in fact multiplied by a differential form will allow to integrate, hence its name.
