Mathematical & Computational Physics

The linear algebra problem of finding non-zero eigenvectors v that, when operated on by a linear operator Â, yield a scalar multiple λ of…

Â v = λ v, det(A - λ I) = 0 Eigenvalues λ (Scalar Units)

Special vectors v associated with a linear transformation matrix A that maintain their spatial direction when operated on, scaled only by…

A v = λ v (where v ≠ 0) Linear Algebra Object

Mathematical & Computational Physics

The mathematical evaluation of how uncertainties in measured input variables propagate into the final calculated physical quantity.

σ_f² = ∑ (∂f / ∂x_i)² σ_x_i² + 2 ∑ (∂f/∂x_i)(∂f/∂x_j) Cov(x_i, x_j) Uncertainty Units

Mathematical & Computational Physics

A basic first-order numerical procedure for solving ordinary differential equations with a given initial value.

y_(n+1) = y_n + h f(t_n, y_n) First-Order Numerical ODE Integration

Mathematical & Computational Physics

The fundamental partial differential equation of the calculus of variations that a function must satisfy to make a functional stationary.

(d / dt) (∂L / ∂q̇_i) - (∂L / ∂q_i) = 0 Calculus of Variations Equation