Mike_bb's latest activity

Could you explain how to derive this formula?

You can define a vector field as follows. Assume that in any coordinates ##x=(x^1,\ldots,x^m)## in a domain ##D\subset\mathbb{R}^m##...

fresh_42 martinbn Big thanks!! :smile:

The book defines vectora and vector fields in the begining. This part is to define the curl of a vector field or the rot (вихрь). The...

I wouldn't use "higher terms equal 0". Instead, think of the standard example of a vector field, a tangent field. It consists of...

In its most abstract form, a vector field is a basis set ##B## of points and a vector ##\vec{v}_p## attached to each point ##p## of...

I didn't miss it. Your question was all about the higher terms, and I answered that instead of looking at higher-order terms and...

Yes. I like Weierstrass's notation of a derivative: ##f## is differentiable at ##x_0## if there is a linear map ##J##, such that...

I'm not sure if it's so but the book uses such terms as "very small element f" = "infinitesimal element f" in context of vector ##V##...

You missed one thing that I wrote in post #1. I mentioned about Taylor series as it was written in the book.

The book doesn't use such terms as "tangent space" and "manifold" quite. The book contains a chapter that is devoted to an introduction...

Russian book "Theory of electricity". https://scask.ru/k_book_tel.php?id=19 page 38

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series...

It's a little hard to say what went wrong because you haven't given any detail of what you actually did. The first bit I understand...

In which case only partial derivatives of ##A_x## can multiply ##\vec{\hat{x}}'##. That doesn't seem plausible, particularly if you...