Mathematical tools for thermodynamics 1
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# Mathematical tools for thermodynamics 1

For beginners one of the best way to begins thermodynamics, In the form of direct application, with detailed quiz answer
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0.0 (0 ratings)
372 students enrolled
Last updated 8/2017
English
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Includes:
• 4 hours on-demand video
• 9 Articles
• Access on mobile and TV
• Certificate of Completion
What Will I Learn?
• Learn polar coordinates
• Ability to calculate a partial derivative
• Know when a differential is exact or not
• Determine a function from its total differential
• Know what it is a state equation
• Ability to calculate an easy path integral
• And in the end it's about training his brain
View Curriculum
Requirements
• Basic calculus, basic algebra ( like a+a=2a, a*a=a²).
• Basic analysis (like derivative of function of one variable).
• Basis integral calculus.
• High school math level.
Description

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.

Who is the target audience?
• Everybody who loves physics
• People who study thermodynamics for the first time
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Curriculum For This Course
32 Lectures
03:45:26
+
Partial derivative and mixte second order partial derivative
12 Lectures 59:11
Preview 12:33

Polar coordinate
1 question

Preview 00:00

Preview 07:17

Quiz 2
7 questions

Preview 00:03

Preview 07:53

Preview 08:27

Quiz 3
1 question

Preview 00:00

Preview 11:18

Quiz 4
1 question

Preview 00:00

Derivative
7 questions

Explanation of quiz 2
00:03

Preview 11:32

Quiz 6
4 questions

Explanation of quiz 6
00:02
+
Exact differential form and Integral of a function of two variables
9 Lectures 01:09:23
Differential form
09:21

Exact differential form
08:44

Quiz 7
7 questions

Explanation of quiz 7
00:00

Exact differential form, part 2
16:11

Quiz 8
2 questions

Explanation of quiz 8
00:00

Integral of a function of two variables, part 1
11:52

Integral of a function of two variables, part 2
13:14

Quiz 9
6 questions

Explanation of quiz 9
00:02

Integral of a function of two variables, part 3
09:58

Quiz 10
1 question
+
State function
2 Lectures 29:40
Integral of a function of two variables, other example
18:02

Quiz 11
4 questions

State function
11:38

Quiz 12
2 questions
+
Application
9 Lectures 01:07:24
Questions
02:07

Simple example of path integral, part 1
09:26

Simple example of path integral, part 2
09:05

Simple example of path integral, part 1
09:41

Remark
10:47

Exact differential form, again
10:21

Quiz 13
1 question

Exact differential form, again and again
05:25

Exact differential form, again and again and again ( no more after that...)
06:40

Integrating factor
03:52