The Divergence of a Vector Field
DOWNLOAD
FREE
|
The divergence of a vector field
Let [Equation goes here - download the original pdf to see it.] be a differentiable vector function, where [Equation goes here - download the original pdf to see it.] are Cartesian coordinates; then the function [Equation goes here - download the original pdf to see it.] is called the divergence of v. Using the nabla, [Equation goes here - download the original pdf to see it.], notation this is [Equation goes here - download the original pdf to see it.] This formula is for computational convenience and is based on the understanding that in the product [Equation goes here - download the original pdf to see it.] the expression [Equation goes here - download the original pdf to see it.] means taking the partial derivative. Example If [Equation goes here - download the original pdf to see it.] find div v Solution [Equation goes here - download the original pdf to see it.]
|
Contents of
The Divergence of a Vector Field
1 The divergence of a vector field
2 Invariance of divergence
3 The divergence and the Laplacian
4 Continuity equation of a compressible fluid flow
|
