Thus, after substitution, the formula relating the derivative of a vector function in two reference frames is
2.
Where represents the unknown vector function, } } is a diagonal matrix of diffusion coefficients, and accounts for all local reactions.
3.
In 1910 he obtained a Ph . D . with a thesis entitled, " Vector Functions of a Point ."
4.
Let " s " be the function mapping the sphere to itself, and let " v " be the tangential vector function to be constructed.
5.
Having single character names for SIMD vector functions is one way that APL enables compact formulation of algorithms for data transformation such as computing Conway's Game of Life in one line of code.
6.
In the following example, the electric field produced by a distribution of charges given by the volume charge density ) } } is obtained by a " triple integral " of a vector function:
7.
Note that \ mathbf { g } has units of acceleration and is a vector function of location relative to the large body, independent of the magnitude ( or even the presence ) of the smaller mass.
8.
Where " " is the divergence operator ( also symbolized " div " ) which maps vector functions to scalar functions, and " is the gradient operator ( also symbolized " grad " ) which maps scalar functions to vector functions.
9.
Where " " is the divergence operator ( also symbolized " div " ) which maps vector functions to scalar functions, and " is the gradient operator ( also symbolized " grad " ) which maps scalar functions to vector functions.
10.
In a sense, both the gradient and Jacobian are " first derivatives " the former the first derivative of a " scalar function " of several variables, the latter the first derivative of a " vector function " of several variables.
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