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The curl of a 3-dimensional vector field which only depends on 2 coordinates (say x and y) is simply a vertical vector field (in the z direction) whose magnitude is the curl of the 2-dimensional vector field, as in the examples on this page. Considering curl as a 2-vector field (an antisymmetric 2-tensor) has been used to generalize vector ...
C: curl, G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist.
def – define or definition. deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform.
Examples of proper fractions are 2/3, –3/4, and 4/9; examples of improper fractions are 9/4, –4/3, and 3/3. improper integral In mathematical analysis , an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number , ∞ {\displaystyle \infty } , − ∞ ...
A vector operator is a differential operator used in vector calculus.Vector operators include: Gradient is a vector operator that operates on a scalar field, producing a vector field.
Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R n), axes (lines through the origin in R n) or rotations in R n. More generally, directional statistics deals with observations on compact Riemannian manifolds including the ...
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
In the context of proofs, this phrase is often seen in induction arguments when passing from the base case to the induction step, and similarly, in the definition of sequences whose first few terms are exhibited as examples of the formula giving every term of the sequence. necessary and sufficient