Beginning with the formal definition of limits, this chapter develops differential and integral calculus in one and several variables, interleaving symbolic derivations with numerical approximations such as automatic differentiation, finite differences, and adaptive quadrature. Multivariate gradients, Jacobians, and Hessians are computed for optimisation problems, while line, surface, and volume integrals bring Stokes’ and Gauss’ theorems to life through vectorised Python code and richly annotated plots.