7.10.3  math.inc - Vector Analysis

SetGradientAccuracy(Value): all below macros make use of a constant named '__Gradient_Fn_Accuracy_' for numerical approximation of the derivatives. This constant can be changed with the macro, the default value is 0.001.

fn_Gradient(Fn): macro calculating the gradient of a function as a function.
Parameters:

• Fn = function to calculate the gradient from.

Output: the length of the gradient as a function.

fn_Gradient_Directional(Fn, Dir): macro calculating the gradient of a function in one direction as a function.
Parameters:

• Fn = function to calculate the gradient from.
• Dir = direction to calculate the gradient.

Output: the gradient in that direction as a function.

fn_Divergence(Fnx, Fny, Fnz): macro calculating the divergence of a (vector) function as a function.
Parameters:

• Fnx, Fny, Fnz= x, y and z components of a vector function.

Output: the divergence as a function.

vGradient(Fn, p0): macro calculating the gradient of a function as a vector expression.
Parameters:

• Fn = function to calculate the gradient from.
• p0 = point where to calculate the gradient.

Output: the gradient as a vector expression.

vCurl(Fnx, Fny, Fnz, p0): macro calculating the curl of a (vector) function as a vector expression
Parameters:

• Fnx, Fny, Fnz = x, y and z components of a vector function.
• p0 = point where to calculate the gradient.

Output: the curl as a vector expression

Divergence(Fnx, Fny, Fnz, p0): macro calculating the divergence of a (vector) function as a float expression
Parameters:

• Fnx, Fny, Fnz = x, y and z components of a vector function.
• p0 = point where to calculate the gradient.

Output: the divergence as a float expression.

Gradient_Length(Fn, p0): macro calculating the length of the gradient of a function as a float expression.
Parameters:

• Fn = function to calculate the gradient from.
• p0 = point where to calculate the gradient.

Output: the length of the gradient as a float expression.

Gradient_Directional(Fn, p0, Dir): macro calculating the gradient of a function in one direction as a float expression.
Parameters:

• Fn = function to calculate the gradient from.
• p0 = point where to calculate the gradient.
• Dir = direction to calculate the gradient.

Output: the gradient in that direction as a float expression