Mathematical & Computational Physics
5 terms
Lagrangian Formalism
Mathematical & Computational Physics
Joules (Action S in J·s)
A formulation of classical mechanics where system dynamics are derived from a single scalar function, the Lagrangian L(q, q̇, t).
L = T - V (Kinetic Energy minus Potential Energy)
Laplace Transform
Mathematical & Computational Physics
s = σ + i ω (Complex Frequency Domain)
An integral transform that maps a real-valued time-domain function f(t) into a complex frequency-domain function F(s).
L{f(t)} = F(s) = ∫₀^(∞) f(t) e^(-s t) dt
Least Squares Data Fitting
Mathematical & Computational Physics
Statistical Regression Method
A standard mathematical regression technique for determining the best-fitting curve or line to a set of data points by minimizing the sum of squared residual deviations.
Minimizing S = ∑_(i=1)^(N) (y_i - f(x_i, β))²
Legendre Polynomials
Mathematical & Computational Physics
Dimensionless Orthogonal Polynomials
A sequence of orthogonal polynomials satisfying Legendre's differential equation (1-x²) y'' - 2x y' + n(n+1) y = 0.
P_n(x) = (1 / (2^n n!)) (d^n / dx^n) ((x² - 1)^n)
Linear Algebra
Mathematical & Computational Physics
Vector Spaces & Matrices
The mathematical discipline studying vector spaces, linear transformations, matrices, and systems of linear equations.
A x = b, v · w = ∑ v_i w_i