NomenclatureEdit
ODE 
Ordinary Differential Equation 
PDE 
Partial Differential Equation 
BC 
Boundary Condition 
IVP 
Initial Value Problem 
BVP 
Boundary Value Problem 
IBVP 
Initial Boundary Value Problem 
Common OperatorsEdit
Operators are shown applied to the scalar or the vector field .
Notation 
Common names and other notation 
Description and notes 
Definition in Cartesian coordinates 

Partial derivative, 
The rate of change of with respect to , holding the other independent variables constant. 


Derivative, total derivative, 
The rate of change of with respect to . If is multivariate, this derivative will typically depend on the other variables following a path. 


Gradient, del operator, 
Vector that describes the direction and magnitude of the greatest rate of change of a function of more than one variable. The symbol is called nabla. 


Laplacian, Scalar Laplacian, Laplace operator, 
A measure of the concavity of , equivalently a comparison of the value of at some point to neighboring values. 


Divergence, 
A measure of "generation", in other words how much the vector field acts as a source or sink at a point. 


Curl, rotor, circulation density, 
A vector that describes the rate of rotation of a (normally 3D) vector field and the corresponding axis of rotation. 


Vector Laplacian 
Similar to the (scalar) Laplacian. Note however, that it is generally not equal to the elementbyelement Laplacian of a vector. 

3D Operators in Different Coordinate SystemsEdit