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Flashcards in Differential vector operators Deck (9)
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1

Define the vector field ∇φ

∇φ is the gradient of φ. It always points toward the direction of maximum increase of φ

2

Give the equation of the directional derivative of φ along u

α is the angle between u and ∇φ

|∇φ| is the magnitude of ∇φ

3

Give the equation of the gradient of a rotationally symmetric scalar field φ(r) = f(r)

êr is the unit vector along the direction of r 

4

Define dr

5

Give the equation of the total differential of a scalar field

 φ(r) = φ(x, y, z)

6

Give the equation of the total differential of a vector field A(r)

7

Define the divergence of the vector field A(r

8

Define the curl of the vector field A(r) 

9

Define the Laplace operator 

The Laplace operator applied to a scalar field φ is called the Laplacian