In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates...

{\displaystyle M} of dimension n {\displaystyle n} , a volume form is an n {\displaystyle n} -form. It is an element of the space of sections of the line bundle...

representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement...

theorem). A representative disc is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length...

{y^{2}}{|cz+d|^{4}}}}={\frac {dz\,d{\overline {z}}}{y^{2}}}.} The invariant volume element is given by d μ = d x d y y 2 . {\displaystyle d\mu ={\frac {dx\,dy}{y^{2}}}...

proof of the volume formula. The volume of the n-ball V n ( R ) {\displaystyle V_{n}(R)} can be computed by integrating the volume element in spherical...

has area element d A = r 2 sin ⁡ θ d θ d φ {\displaystyle dA=r^{2}\sin \theta \,d\theta \,d\varphi } . This can be found from the volume element in spherical...

corresponding density function. Often the volume integral is represented in terms of a differential volume element d V = d x d y d z {\displaystyle dV=dx\...

three-dimensional bodies. A 'unit' of infinitesimally small volume in integral calculus is the volume element; this formulation is useful when working with different...

pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling...

{\displaystyle \sigma _{q}={\frac {dQ}{dS}}\,,} and the volume charge density uses a volume element dV ρ q = d Q d V , {\displaystyle \rho _{q}={\frac {dQ}{dV}}\...

Area element Divergence theorem Stokes' theorem Line integral Line element Volume element Volume integral Cartesian coordinate system Volume and surface...

In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in...

Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and g the standard gravity, then:...

the volume of the spherical differential volume element. Unlike rectangular differential volume element's volume, this differential volume element's volume...

_{3}\mathbf {e} _{3}=-1.} Moreover, the volume element e 123 {\displaystyle \mathbf {e} _{123}} commutes with any other element of the C ℓ ( 3 ) {\displaystyle...

where ρ2 = ρ(x, y, z) is the mass density at the volume element and of the direction from the volume element to point mass 1. u {\displaystyle u} [clarification...

particle occupies a given very small region of space (mathematically the volume element d 3 r {\displaystyle d^{3}\mathbf {r} } ) centered at the position r...

Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical...

based on the concept of the representative volume element (RVE). An RVE is understood to be a sub-volume of an inhomogeneous medium that is of sufficient...

depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. In the diagram, everything...

an abbreviated term for a "surface element," analogous to a "voxel" (volume element) or a "pixel" (picture element). In 3D computer graphics, the use...

the volume of the control volume element, and A {\displaystyle \mathbf {A} } is the surface area of the control volume element. The finite element method...

\theta ,\\r^{2}&=ax^{2}+by^{2}+cz^{2}.\end{aligned}}} An infinitesimal volume element is given by d V = | ∂ ( x , y , z ) ∂ ( r , θ , φ ) | d r d θ d φ =...

_{V}\mathbf {f} (\mathbf {r} )\mathrm {d} V\,,} where dV is an infinitesimal volume element, and f is the external body force density field acting on the system...

small volume element ΔV (i.e. locally) but the electron density n ( r ) {\displaystyle n(\mathbf {r} )} can still vary from one small volume element to the...

{\displaystyle \mathbf {f} =-\nabla p} . The net force on a differential volume element dV of the fluid is: d F = f d V {\displaystyle d\mathbf {F} =\mathbf...

manifolds, one cannot define a volume form globally due to the non-orientability, but one can define a volume element, which is formally a density, and...

stresses do not exert a torque on the volume element, the resultant force must lead through the center of the volume element. The line of action of the inertia...

{\displaystyle \mathbf {r} -\mathbf {r'} } is the vector that points from the volume element d 3 r ′ {\displaystyle \mathrm {d^{3}} \mathbf {r'} } to the point in...