Mathematical & Computational Physics
3 terms
Spherical Harmonics
Mathematical & Computational Physics
Spherical Surface Functions
A set of special orthogonal functions defined on the 2D sphere surface serving as angular solutions to Laplace's equation in 3D spherical coordinates.
Y_l,m(θ, φ) = √(((2l+1)/(4π)) ((l-m)!/(l+m)!)) P_l^m(cos θ) e^(i m φ)
Statistics and Probability
Mathematical & Computational Physics
Probability (0 to 1)
The mathematical frameworks for analyzing random phenomena, quantifying measurement uncertainty, and modeling ensemble behavior in statistical mechanics.
P(A|B) = P(B|A) P(A) / P(B), μ = E[X], σ² = Var(X)
Stokes' Theorem
Mathematical & Computational Physics
Vector Line/Surface Integral Equality
A fundamental vector calculus theorem relating the surface integral of the curl of a vector field over an open surface S to the line integral of the field around its boundary curve ∂S.
∮_(∂S) F · dr = ∬_S (∇ × F) · dA