- #1

jacobrhcp

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[tex]\nabla\bullet(x_{i}a)=div(x_{i}a)=\partial_{j}a_{j}x_{i}=3x_{i}[/tex]

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- Thread starter jacobrhcp
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In summary, The conversation is about using the Einstein convention to calculate explicitly the partial derivatives of \nabla \bullet (x_{i}\vec{a}). The notation x_{i}\vec{a} is clarified and it is determined that the answer is \partial_{j} (a_{j}x_{i}), which simplifies to a_j \partial_{j} x_{i}.

- #1

jacobrhcp

- 169

- 0

[tex]\nabla\bullet(x_{i}a)=div(x_{i}a)=\partial_{j}a_{j}x_{i}=3x_{i}[/tex]

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- #2

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The partial derivatives are take wrt what variable ? x or a ?

- #3

jacobrhcp

- 169

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it's said x above the exercises [tex]\partial_{j}=\frac{\partial}{\partial x_{j}}}[/tex]

and the question is:

calculate explicitly: [tex]\nabla \bullet (x_{i}\vec{a})[/tex], where a is a constant vector...

my attempt is way off, but I don't feel at home in these new symbols enough to get the right answer.

and the question is:

calculate explicitly: [tex]\nabla \bullet (x_{i}\vec{a})[/tex], where a is a constant vector...

my attempt is way off, but I don't feel at home in these new symbols enough to get the right answer.

Last edited:

- #4

pam

- 458

- 1

[xa], or does it mean [tex]{\vec\hat i}\cdot{\vec r}{\vec a}[/tex]?

- #5

kdv

- 348

- 6

jacobrhcp said:

[tex]\nabla\bullet(x_{i}a)=div(x_{i}a)=\partial_{j}a_{j}x_{i}=3x_{i}[/tex]

You are right that it means [tex] \partial_{j} (a_{j}x_{i}) [/tex] But the components of a are constants so this is equal to [tex]a_j \partial_{j} x_{i} [/tex] Now, what does [tex] \partial_{j} x_{i} [/tex]give ?

A tensor in calculus is a mathematical object used to describe relationships between different quantities in multi-dimensional space. It is represented by an array of numbers and has certain properties that allow it to be manipulated algebraically.

Tensors in calculus are typically represented using index notation, where indices are used to denote the position of each element in the tensor array. The number of indices corresponds to the number of dimensions in the space being described.

The notation used to represent tensors in calculus can be complex and difficult to understand, leading to confusion and potential errors in calculations. Additionally, there are multiple notations used by different fields of study, making it challenging for scientists to communicate and collaborate.

One way to address the notational problem in tensor calculus is to use a standardized notation that is widely accepted by the scientific community. This can help improve communication and understanding between researchers. Additionally, there are efforts to develop more intuitive notations for tensors, such as graphical representations.

Some common mistakes when working with tensors in calculus include forgetting to include all necessary indices, incorrectly contracting or multiplying tensors, and not understanding the properties of tensors. It is important to carefully follow the rules and properties of tensors to avoid errors in calculations.

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