Gradients vs. Partial Derivatives

[shanepitts]

What is the difference between partial derivatives and gradients, if there is any?

I'm asking because I need to derive a function " f (T,P) " for air convection; where T is temperature and P is pressure and both are variables in this case.

Thanks

 

[micromass]

A gradient is the matrix containing all the partial derivatives.

 

[HallsofIvy]

For a function of three variables, grad F(x,y,z)= \nabla F(x, y, z)= \frac{\partial F}{\partial x}\vec{i}+ \frac{\partial F}{\partial y}dy\vec{j}+ \frac{\partial F}{\partial z}\vec{j}. In particular, the differential, dF= \frac{\partial F}{\partial x}dx+ \frac{\partial F}{\partial y}dy+ \frac{\partial F}{\partial z}dz, can be thought of as the dot product of \nabla F and dx\vec{i}+ dy\vec{j}+ dz\vec{k}.

 

[GiuseppeR7]

What is the difference between partial derivatives and gradients, if there is any?

I'm asking because I need to derive a function " f (T,P) " for air convection; where T is temperature and P is pressure and both are variables in this case.

Thanks

partial derivatives are "limits" meanwhile the gradient is an operator.