いろんな式

Φⁿ⁺¹ = Φⁿ + Δt ((3/2)f(Φⁿ) - (1/2)f(Φ^n-1))

<∇Φ>_i = (d / n₀) Σ ((Φ_j - Φ_i) / | r_j - r_i | ²) (r_j - r_i) w(| r_j - r_i |)

<∇²Φ>_i = (2 d / n₀ λ) Σ (Φ_j - Φ_i) w(| r_j - r_i |)

λ = ∫_V w(r) r² dv / ∫_V w(r) dv

n₀ = Σ w(| r_j - r_i |)

(w,x,y,z) = (cos(θ/2),n_xsin(θ/2),n_ysin(θ/2),n_ysin(θ/2))

∫_V ∇⋅F dV = ∫_∂V F⋅dS

ω = dΩ/dt

v = ω×r

M = r×F = I dω/dt

I = ∫ r^2 dm

(a, u)(b, v) = (ab - u⋅v, av + bu + u×v)

∫_C ∇×F⋅dS = ∫_∂C F⋅ds

(1/σ√2π) exp ( - (x - μ)² / 2σ²)

f(x) = Σ ( f⁽ⁿ⁾(a) / n! ) (x - a)ⁿ

∂u/∂t + u ⋅ ∇u = f - ∇(p/ρ) + ν ∇²u

p + (1/2)ρ v² + ρ g h = const.

s = (a + b + c) /2

S = √s (s-a) (s-b) (s-c)

f(ξ) = max_{g(x) = 0} f(x)

h(x,λ) = f(x) - λg(x)

∀i ∂h(ξ,λ)/∂x_i = 0 ∧ ∂h(ξ,λ)/∂λ = 0

J = ((v_2- - v_1-) ⋅ n) (e + 1) / (1/m₁ + 1/m₂)

v₁₊ = v_1- + J n / m₁

v₂₊ = v_2- - J n / m₂