Mathematical tools for continuum mechanics

In summary, a person is seeking help in finding the necessary mathematical tools for studying continuum mechanics. They specifically mention needing knowledge in ODEs, PDEs, differential geometry, and vector calculus. They also mention struggling with understanding tensors and ask for recommendations on resources to learn more about them. They mention trying to search for resources but not finding what they need. A recommendation is made for the book "Functional and Structured Tensor Analysis for Engineers" and a link is provided for a document on tensor analysis that the person found helpful.
  • #1
Pressure
2
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
Vector-Tensor calculus, PDEs, with whatever physics is necessary. A good first start is the FREE book:
"Functional and Structured Tensor Analysis For Engineers"
 
  • #5

1. What is continuum mechanics?

Continuum mechanics is a branch of mechanics that deals with the study of materials and objects that can be modeled as continuous matter, without considering their microscopic structure. It involves the application of mathematical tools to describe the behavior of solids, fluids, and gases under various physical conditions.

2. What are some examples of mathematical tools used in continuum mechanics?

Some common mathematical tools used in continuum mechanics include vector calculus, tensor analysis, differential equations, and variational methods. These tools are used to model and analyze the behavior of materials and objects at a macroscopic level.

3. How are mathematical tools used to solve problems in continuum mechanics?

Mathematical tools are used to formulate equations that describe the behavior of materials and objects in continuum mechanics. These equations can then be solved using numerical methods or analytical techniques to obtain solutions and make predictions about the behavior of the system.

4. Can mathematical tools be applied to all types of materials and objects in continuum mechanics?

Yes, mathematical tools can be applied to a wide range of materials and objects in continuum mechanics, including solids, fluids, and gases. However, the specific equations and techniques used may vary depending on the properties of the material or object being studied.

5. Are there any limitations to using mathematical tools in continuum mechanics?

While mathematical tools are a powerful and widely used approach in continuum mechanics, they may have limitations in certain situations. For example, they may not accurately describe the behavior of highly complex materials or systems, or in cases where the effects of quantum mechanics are significant.

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