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Mathematical & Computational Physics

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Mathematical & Computational Physics

Differential Equation

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 Mathematical Equation Class Mathematical & Computational Physics

Dirac Delta Function

A generalized function (distribution) that is zero everywhere except at x = 0 where it is infinite, with an integral over all space equal…

δ(x) = 0 for x ≠ 0, ∫_(-∞)^(∞) δ(x) dx = 1, ∫ f(x) δ(x - a) dx = f(a) 1 / [x Unit] Mathematical & Computational Physics

Divergence

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) [Vector Field Unit] / m Mathematical & Computational Physics

Divergence Theorem

A fundamental theorem of vector calculus stating that the outward flux of a vector field through a closed surface ∂V equals the volume…

∯_(∂V) F · dA = ∭_V (∇ · F) dV Vector Integral Theorem