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

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...

{\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...

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...

{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}}}...

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...

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...

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...

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...

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

integral Volume element Line element Line integral "Multiple integral", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Weisstein, Eric W. "Volume integral"...

{\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}}\...

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...

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

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

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

depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. The electric fields of the...

{F} \,\!} . The corresponding formula for the transformation of the volume element is d v = J   d V {\displaystyle dv=J~dV} Derivation of Nanson's relation...

{\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...

f(x,y,z){\text{d}}x\wedge {\text{d}}y\wedge {\text{d}}z} represents a volume element that can be integrated over a region of space. In general, a k-form...

conditions (as many particles as flow out of a volume element also flow in steadily, so that the situation in the element appears static), i.e. independent of time...

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

\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 =...

{\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...

nadir, and the choice of azimuthal angle is arbitrary.) To express the volume element of ⁠ n {\displaystyle n} ⁠-dimensional Euclidean space in terms of spherical...

unit of volume (a volume element) as it flows with the vector field. On a pseudo-Riemannian manifold, the divergence with respect to the volume can be...

an oriented plane element and a trivector is an oriented volume element, in the same way that a vector is an oriented line element. Given vectors a, b...

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...