Mathematical notation

Variable: \(x,t,N,I\) — a quantity that can vary.

Parameter: \(\beta,\gamma,r,K\) — a quantity specifying a model, often treated as fixed within one analysis.

Function: \(y=f(x)\) — assigns an output to an input.

Derivative: \(dy/dt\) or \(f'(t)\) — instantaneous rate of change.

Partial derivative: \(\partial u/\partial t\) — derivative with respect to one variable while other independent variables are held fixed.

Expectation: \(E[X]\). Variance: \(\operatorname{Var}(X)\).

Vector: \(\mathbf{x}\). Matrix: \(A=(a_{ij})\). Transpose: \(A^T\).

Summation: \(\sum_{i=1}^n x_i\). Integral: \(\int_a^b f(x)\,dx\).