Open, closed and compact sets in Euclidean space. Matrix norms and equivalence of norms. Limits and continuity in several variables. Curves and path connectedness. Partial and directional derivatives, the gradient and differentiability. The implicit, open and inverse function theorems. Largange multipliers. Optimization: the Hessian matrix and critical points. Multivariable Riemann integration: Fubini’s theorem and the change of variables formula.