(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider scalar functions u = u(x). Compute the gradients ∇u for:

u(x) = (x, y, z)

u(x) = (y, z, x)

u(x) = (x^2y, 10, z + x)

2. Relevant equations

This is a question on my homework for undergraduate Fluid Mechanics. The teacher has been assigning math problems in topics covered in prerequisite courses for homework at the beginning of the semester. He has not explained any of these concepts, and whenever anyone asks he says "Calculus is a prerequisite for this class, you should know this already". Sorry if it sounds like I'm just complaining about my instructor's teaching style, but the point I'm trying to make is that I don't have any examples to look at to help me understand this notation.

I took Calc III about 7 years ago, so I clearly don't remember everything. Through internet research I found out that a gradient is the set of partial derivatives of each variable in a multi-variable function. For example I think I understand (please correct me if I'm wrong) that if

F(x,y,z)=x+3y+z^2

the gradient of F(x,y,z) is (1, 3, 2z)

However, I do not understand this question. It may just be that I do not understand his notation. Is u(x)=(x,y,z) just another way of writing u(x) = x+y+z? Why isn't it u(x,y,z) = (x,y,z), since there are 3 variables? Has anyone seen this notation before?

3. The attempt at a solution

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# Confused about notation for computing gradients

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