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Mathematical & Computational Physics

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Mathematical & Computational Physics

Genetic Algorithms

A search heuristic optimization method inspired by natural biological evolution that iteratively evolves candidate solutions toward optimal…

Evolutionary Operators: Selection, Crossover, Mutation Stochastic Heuristic Optimization Mathematical & Computational Physics

Gradient

A vector operator that points in the direction of the greatest rate of increase of a scalar field, with magnitude equal to that maximum…

∇f = (∂f/∂x) î + (∂f/∂y) ĵ + (∂f/∂z) k̂ [Scalar Field Unit] / m Mathematical & Computational Physics

Gradient Descent

An iterative first-order optimization algorithm for finding local minima of a differentiable scalar objective function by taking steps…

x_(k+1) = x_k - α ∇f(x_k) Iterative Optimization Method Mathematical & Computational Physics

Green's Function

An impulse response function used to solve inhomogeneous linear differential equations subject to specified boundary conditions.

L G(x, x') = δ(x - x'), y(x) = ∫ G(x, x') f(x') dx' Impulse Response Function Mathematical & Computational Physics

Green's Theorem

A 2D vector calculus theorem relating a line integral around a simple closed curve C to a double area integral over the enclosed plane…

∮_C (L dx + M dy) = ∬_D ((∂M/∂x) - (∂L/∂y)) dx dy 2D Vector Integral Theorem Mathematical & Computational Physics

Group Theory

The mathematical study of groups and algebraic symmetry structures.

Group Axioms: Closure, Associativity, Identity, Inverse Symmetry Groups (SO(3), SU(2), SU(3))