Mathematical & Computational Physics

An efficient algorithm that computes the Discrete Fourier Transform (DFT) of a sequence in O(N log N) operations instead of O(N²).

Cooley-Tukey Divide-and-Conquer: O(N log N) vs O(N²) Computational FFT Algorithm

A numerical method for solving differential equations by approximating derivatives with finite difference quotients on a discretized grid.

f'(x) ≈ (f(x + h) - f(x - h)) / (2 h), f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h² Grid Discretization Method

Mathematical & Computational Physics

A numerical technique for solving complex partial differential equations by subdividing a large physical domain into smaller, simpler…

K u = f (Global Stiffness Matrix Equation) Numerical Mesh Method

Mathematical & Computational Physics

An expansion of a periodic function f(x) into an infinite sum of orthogonal sine and cosine harmonic functions.

f(x) = a₀/2 + ∑_(n=1)^(∞) [a_n cos(n x) + b_n sin(n x)] Harmonic Series Expansion

Mathematical & Computational Physics

An integral transform that decomposes a continuous time or spatial signal into its constituent frequency or wavevector spectrum.

f̂(k) = ∫_(-∞)^(∞) f(x) e^(-i k x) dx, f(x) = (1 / 2π) ∫_(-∞)^(∞) f̂(k) e^(i k x) dk Inverse Domain Unit (e.g. s⁻¹ or m⁻¹)