All Questions
4
questions
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If $S$ is a symmetric matrix, then rewriting $\int{S:\nabla \phi} dx$
I am trying to prove that:
If $S$ is a symmetric matrix, then one can rewrite $\int{S:\nabla \phi} \text{dx}$ as $\int{S:D(\phi)} \text{dx}$, where $D(\phi)$ is the symmetric gradient of $\phi$.
Any ...
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1
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Finding the Gradient of a Vector Function by its Components
In Multivariable Calculus, we can easily find the gradient of a scalar function (producing a scalar field) $f : \mathbb{R^n} \to \mathbb{R}$, and the gradient function would produce a vector field.
$$...
- 13.2k
4
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1
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Divergence operator of higher order and intrinsic point of view
Let $\underline{u}$ be a $1$ - order tensor (say a column vector) I want to prove that :
$\underline{\operatorname{div}} \left( (\underline{\underline{\operatorname{grad}}} \, \underline{u})^T\...
- 1,294
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Covariant derivative for a covector field
In the lecture we had the immersion $f: U \subset \mathbb{R}^2 \rightarrow \mathbb{R}^3$.
Now we said that a map $\lambda : U \rightarrow T^*f$ is a covector field. Okay, that's fine.
Also, we ...
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