Search results

The '''Ishimori equation''' is a [[partial differential equation]] proposed by the Japanese [[mathematician]] {{harvtxt|Ishimori|19 ...S}}{\partial y} + \frac{\partial u}{\partial y}\frac{\partial \mathbf{S}}{\partial x},</math>|{{EquationRef|1a}}}} ...

...tle=The Aboodh Transform Techniques to Ulam Type Stability of Linear Delay Differential Equation |url=https://doi.org/10.1007/s40819-023-01577-5 |journal=Internati ...nsform Iterative Method for Solving Time – Fractional Partial Differential Equations |url=https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/ ...

<math display="block"> \frac{\partial}{\partial t}Q = 0\;,</math> ...try. Conserved currents play an important role in the theory of [[partial differential equation]]s, as the existence of a conserved current points to the existenc ...

...surface integral|surface]], d'''S''' is the [[Differential (infinitesimal)|differential]] [[vector area]] element, '''n''' is the [[unit normal]] to the surface. ' ==Equations== ...

...[[electromagnetic wave equation]]s. The equations follow from [[Maxwell's equations]]. == Maxwell's equations == ...

...athbf{E} = -\mathbf{\nabla} \phi - \frac{1}{c} \frac{\partial \mathbf{A}}{\partial t} </math> :<math>F^{\mu\nu} = \partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu} = ...

...charge|charges]] are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast [[Magnetization reversal|magn ===Magnetostatics as a special case of Maxwell's equations=== ...

...|exterior derivative]] of the [[electromagnetic four-potential]], ''A'', a differential 1-form:<ref>{{cite book |author1=J. A. Wheeler |author2=C. Misner |author3= Therefore, ''F'' is a [[differential form|differential 2-form]]—that is, an antisymmetric rank-2 tensor field—on Minkowski space. ...

...l]] length of a small element of a defined curve, the contribution of that differential length to circulation is {{math|dΓ}}: <math display="block">\Gamma = \oint_{\partial S} \mathbf{V}\cdot \mathrm{d}\mathbf{l} = \iint_S \nabla \times \mathbf{V} ...

<math display="block">\hat{E} = i\hbar\frac{\partial}{\partial t} </math> <math display="block">i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = \hat H \Psi(\mathbf{r},t)</math> ...

==Maxwell's original equations== ...ions]], until this term became applied instead to a vectorized set of four equations selected in 1884, which had all appeared in his 1861 paper "[[On Physical L ...

...anings. In the most common acceptance, quasistatic approximation refers to equations that keep a static form (do not involve [[time derivative]]s) even if some ...s to a situation where all time derivatives can be neglected. However some equations can be considered as quasistatic while others are not, leading to a system ...

{{Short description|Equations of electromagnetism}} ...'' charges and currents. They are the particular solutions to [[Maxwell's equations]] for any arbitrary distribution of charges and currents.<ref>[[Oleg D. Jef ...

...plicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines. It is therefore convenient to collect many of thes ...th> and <math>\mathbf{B}</math>. Using [[vector calculus]] and [[Maxwell's equations]], symmetry is sought for in the terms containing <math>\mathbf{E}</math> a ...

...eat equation]], this number system applies to any phenomena described by [[differential equation]]s such as [[diffusion]], [[acoustics]], [[electromagnetics]], [[f | Neumann || <math> \frac{\partial G}{\partial n} = 0 </math> || 2 ...

'''Poisson's equation''' is an [[elliptic partial differential equation]] of broad utility in [[theoretical physics]]. For example, the so ...\partial x^2} + \frac{\partial^2 V} {\partial y^2} + \frac{\partial^2 V} {\partial z^2} = 0, = -2k\pi, = -4k\pi,</math> ...

{{Short description|Partial differential equation used in physics}} ...imensions|three-dimensional form of the wave equation]]. The [[Homogeneous differential equation|homogeneous]] form of the equation, written in terms of either the ...

:<math>\rho_0 \frac{\partial^2 z'}{\partial t^2} = - g \left[\rho (z)-\rho (z+z')\right]</math> ...pproximation]] to <math>\rho (z+z') - \rho (z) = \frac{\partial \rho (z)}{\partial z} z'</math>, and move <math>\rho_0</math> to the RHS: ...

...from one frame to another. However, this is not as general as [[Maxwell's equations in curved spacetime]] or non-rectilinear coordinate systems. ...in a vacuum, one could instead regard them as the formulation of Maxwell's equations in terms of ''total'' charge and current. ...

...n particular, a vector field on <math>\R^3</math> can be considered as a [[differential form|1-form]] in which case its curl is its [[exterior derivative]], a 2-fo ...x, y, z), F_z(x, y, z))</math> is defined and has continuous first order [[partial derivatives]] in a region containing <math>\Sigma</math>, then ...