How Can I Understand Rotor and Partial Derivatives in Multivariable Functions?

[Bruneleski]

Homework Statement

Last week we've been doing partial derivatives and I understood all that , but also skipped last lecture.I asked colleague about the lecture and he told me that professor mentioned something about rotor and he gave an example of such and such problem.Anyway here it goes:
1)Prove that the expression (something)dx+(something)dy+(something)dz is a differential of a function and find that function.
2)Find u(x,y,z) if du=(something)dx+(something)dy+(something)dz
You get the picture.
Now I've looked up about the rotor stuff and found it has something to do with vector fields.So I tell that to my friend but he says lecturer didn't even mention anything like that, he says they used integrals on multivariable functions and so on.
Where I can find out more about these types of problems? What to look for in textbooks?
Thanks.

Homework Equations

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The Attempt at a Solution

I don't know what to look for.

 

[Mark44]

Moved thread, as this seems to me to be more of a conceptual question rather than a specific homework question.

 

[MarcusAgrippa]

The equation du = P(x,y,z) dx + Q(x,y,z) dy + R(x,y,z) dz is a key equation and is the starting point for many important topics. You will find the equation described in any book on differential equations. Try Piaggio - an old book, but useful. This equation does not always admit solutions and there are integrability conditions that will tell you when a solution does exist. When solutions exist, there are several methods for finding them. A simple one is called Mayer's method in Piaggio's book.

The discussion of this equation is too long for this forum. You are effectively asking for an entire lecture. If after reading up the material you have more specific questions, those could be tackled here.

 

[Mark44]

The discussion of this equation is too long for this forum. You are effectively asking for an entire lecture. If after reading up the material you have more specific questions, those could be tackled here.

+1