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Gradients vs. Partial Derivatives

  1. Oct 11, 2015 #1
    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
     
  2. jcsd
  3. Oct 11, 2015 #2

    micromass

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    A gradient is the matrix containing all the partial derivatives.
     
  4. Oct 12, 2015 #3

    HallsofIvy

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    For a function of three variables, grad [itex]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}[/itex]. In particular, the differential, [itex]dF= \frac{\partial F}{\partial x}dx+ \frac{\partial F}{\partial y}dy+ \frac{\partial F}{\partial z}dz[/itex], can be thought of as the dot product of [itex]\nabla F[/itex] and [itex]dx\vec{i}+ dy\vec{j}+ dz\vec{k}[/itex].
     
  5. Oct 16, 2015 #4
    partial derivatives are "limits" meanwhile the gradient is an operator.
     
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