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Having a bit of trouble comprehending the following expression in suffix notation:

F_{j} (∂/∂x_{i})G_{j}

Now it's a sum over j so its

F_{1}(∂/∂x_{i})G_{1} + F_{2}(∂/∂x_{i})G_{2} + F_{3}(∂/∂x_{i})G_{3}

= (F_{1}, F_{2}, F_{3}).((∂/∂x_{i})G_{1}, (∂/∂x_{i})G_{2}, (∂/∂x_{i})G_{3})

= F . ((∂/∂x_{i})G_{1}, (∂/∂x_{i})G_{2}, (∂/∂x_{i})G_{3})

What is the second bracket? Is it div(G) (i.e factoring out the (∂/∂x_{i}) gives (∂/∂x_{i})G )

Or is it (grad G_{1}, grad G_{2}, grad G_{3})?

F

Now it's a sum over j so its

F

= (F

= F . ((∂/∂x

What is the second bracket? Is it div(G) (i.e factoring out the (∂/∂x

Or is it (grad G

The monster you have there is something called a tensor - but don't worry about that because you don't need to know it yet. The key to understanding it is to treat the bracket with the Gs like a 3x3 matrix where the ij^{th} element is $\frac{\partial G_j}{\partial x_i}$, and treat F as a vector, and just multiply them out in the appropriate manner. This is what you'd expect - the expression you start with has one free index, so it'll look like a vector.

I think that what's confusing you is that there isn't a common representation for this particular combination. It's not grad or div or anything like that - it's just somethign on its own. There isn't really a nice way to think about it. It took me ages to get to grips with some of the dodgy constructions you get with suffix notation!

I think that what's confusing you is that there isn't a common representation for this particular combination. It's not grad or div or anything like that - it's just somethign on its own. There isn't really a nice way to think about it. It took me ages to get to grips with some of the dodgy constructions you get with suffix notation!

Cexy

I think that what's confusing you is that there isn't a common representation for this particular combination. It's not grad or div or anything like that - it's just somethign on its own.

Yeah, exactly! I'm still struggling to recognise things straight away in terms of suffix notation, so I want to be able to think about what an expression means in terms of recognizable notation... But if there isn't one, that's fine. Thank's a lot for clearing that up!

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can someone please explain what principle domain is and why the answer is a not c?Maths

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