Mathematical & Computational Physics
4 terms
Differential Equation
Mathematical & Computational Physics
Mathematical Equation Class
A mathematical equation relating an unknown function to its derivatives with respect to one or more independent variables.
F(x, y, y', y'', ..., y^(n)) = 0, d²y/dx² + ω² y = 0
Dirac Delta Function
Mathematical & Computational Physics
1 / [x Unit]
A generalized function (distribution) that is zero everywhere except at x = 0 where it is infinite, with an integral over all space equal to 1.
δ(x) = 0 for x ≠ 0, ∫_(-∞)^(∞) δ(x) dx = 1, ∫ f(x) δ(x - a) dx = f(a)
Divergence
Mathematical & Computational Physics
[Vector Field Unit] / m
A scalar differential operator measuring the net outward flux density of a vector field from an infinitesimal volume around a given point.
div F = ∇ · F = (∂F_x/∂x) + (∂F_y/∂y) + (∂F_z/∂z)
Divergence Theorem
Mathematical & Computational Physics
Vector Integral Theorem
A fundamental theorem of vector calculus stating that the outward flux of a vector field through a closed surface ∂V equals the volume integral of its divergence over the enclosed region V.
∯_(∂V) F · dA = ∭_V (∇ · F) dV