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ENgez

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Background: I am currently reading up on homogenization theory.

I have a simple conductivity model (image attached). u is a scalar function (such as potential or temperature).

The textbook proceeds by giving a series expansion for the gradient of u (image attached). the problem is that the gradient is supposed to be a vector function, and the one given is a scalar (pretty sure that the expression given by the book is the differential)

The fact that the gradient is supposedly a scalar makes the divergence operation in the model undefined, which basically makes all following math in the book unclear to me..

How to makes sense of it?

I have a simple conductivity model (image attached). u is a scalar function (such as potential or temperature).

The textbook proceeds by giving a series expansion for the gradient of u (image attached). the problem is that the gradient is supposed to be a vector function, and the one given is a scalar (pretty sure that the expression given by the book is the differential)

The fact that the gradient is supposedly a scalar makes the divergence operation in the model undefined, which basically makes all following math in the book unclear to me..

How to makes sense of it?