Mathematical tools for continuum mechanics

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Discussion Overview

The discussion focuses on the mathematical tools necessary for studying continuum mechanics, including the foundational concepts and resources for learning. Participants share their experiences and suggest materials for further study.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants suggest that essential mathematical tools for continuum mechanics include ordinary differential equations (ODEs), partial differential equations (PDEs), differential geometry, and vector calculus.
  • One participant expresses confusion about the introduction to tensors in their class, noting that the concept was not adequately covered, and questions the necessity of knowing more about tensor analysis.
  • Another participant recommends a free book titled "Functional and Structured Tensor Analysis For Engineers" as a good starting point for learning tensor analysis.
  • A participant provides a link to a document on tensor analysis that they found helpful, suggesting it is presented in an effective manner for learning.

Areas of Agreement / Disagreement

Participants generally agree on the importance of tensor analysis for continuum mechanics, but there is no consensus on the specific resources or the depth of knowledge required.

Contextual Notes

Some participants express uncertainty regarding the adequacy of their current educational resources and the clarity of concepts introduced in their classes. There are mentions of missing foundational knowledge that may impact understanding.

Who May Find This Useful

This discussion may be useful for students and professionals in engineering or physics who are beginning to study continuum mechanics and are seeking guidance on necessary mathematical tools and resources.

Pressure
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Hello^^ (I'm new here)
I want to know the mathematical tools i need to study continuum mechanics.
It would be great if someone give me a link that contains video lectures.
Thanks for help .
 
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Pressure said:
Hello^^ (I'm new here)
I want to know the mathematical tools i need to study continuum mechanics.
It would be great if someone give me a link that contains video lectures.
Thanks for help .
The tools you need for continuum mechanics are ODE's, PDE's, differential geometry, and vector calculus.
 
Hello,
Thanks for your ansewr.
We started in class" Mécanique des milieux continus " which i translated to "Continuum mechanics".
We started by talking about the concept of deformation of a solid, about the tensor gradient of transfomation...
But it was introduced in a poor way (in class): we didn't even talk about what a tensor is..!(we took it as matrix)
...
The introduction was insufficient.. and things are vague, not rigourous and not clear to me!
So, please:
Could you tell me if i will need to know more about tensor analysis?
I'm confused about what i should ask you, but i want to know from your experiences the things that an engineer has to know...or.. (a link, a PDF, a video lecture)

PS: I tried to search in MIT ocw but couldn't find exactly what i need.
Sorry for my being not clear and thank you.
 
Vector-Tensor calculus, PDEs, with whatever physics is necessary. A good first start is the FREE book:
"Functional and Structured Tensor Analysis For Engineers"
 

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