Mathematical & Computational Physics
5 terms
Fast Fourier Transform (FFT)
Mathematical & Computational Physics
Computational FFT Algorithm
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)
Finite Difference Method
Mathematical & Computational Physics
Grid Discretization Method
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
Finite Element Method (FEM)
Mathematical & Computational Physics
Numerical Mesh Method
A numerical technique for solving complex partial differential equations by subdividing a large physical domain into smaller, simpler finite sub-domains called elements.
K u = f (Global Stiffness Matrix Equation)
Fourier Series
Mathematical & Computational Physics
Harmonic Series Expansion
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)]
Fourier Transform
Mathematical & Computational Physics
Inverse Domain Unit (e.g. s⁻¹ or m⁻¹)
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