Integration of the normal probability density function of the velocity, above, over the course ( from 0 to 2 \ pi ) and path angle ( from 0 to \ pi ), with substitution of the speed for the sum of the squares of the vector components, yields the speed distribution.

42.

A key feature of the representation of vectors and tensors in terms of indexed components and basis vectors is " invariance " in the sense that vector components which transform in a covariant manner ( or contravariant manner ) are paired with basis vectors that transform in a contravariant manner ( or covariant manner ).

43.

Several authors work with reflection " on " a vector ( negating all vector components except that parallel to the specifying vector ), while others work with reflection " along " a vector ( negating only the component parallel to the specifying vector, or reflection in the hypersurface orthogonal to that vector ).

44.

:: Isn't it more usual to use ( i, j ) and ( i, j, k ) to describe 2D and 3D floating vector components, so that the ( x, y ) and ( x, y, z ) coords can be added to describe the endpoint of a 2D or 3D fixed vector?

45.

However, the observed fine structure when the electron is observed along one axis, such as the " z "-axis, is quantized in terms of a magnetic quantum number, which can be viewed as a quantization of a vector component of this total angular momentum, which can have only the values of "' " } }.

46.

The FDTD method belongs in the general class of leapfrog manner : the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved.

47.

The FDTD method belongs in the general class of leapfrog manner : the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved.

48.

Maxwell's equations " seem " overdetermined, in that they involve six unknowns ( the three components of and ) but eight equations ( one for each of the two Gauss's laws, three vector components each for Faraday's and Ampere's laws ) . ( The currents and charges are not unknowns, being freely specifiable subject to charge conservation . ) This is related to a certain limited kind of redundancy in Maxwell's equations : It can be proven that any system satisfying Faraday's law and Ampere's law " automatically " also satisfies the two Gauss's laws, as long as the system's initial condition does.

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