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...

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...

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}}}...

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...

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

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

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\...

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...

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...

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...

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

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...

{\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}}\...

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

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...

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

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...

\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 =...

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...

{\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} \,\!} . 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...

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...

molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum...

Mercury is a chemical element; it has symbol Hg and atomic number 80. It is commonly known as quicksilver. A heavy, silvery d-block element, mercury is 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...

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

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...