Mathematical tools for thermodynamics 1

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 derivative
• Mixed second partial derivative
• differential form
• integral of function of two variables
• notion of state function
• path integral
• integrating 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.