Pointwise convergence of sequences and of series of functions. Functions of several variables: limits, continuity, directional derivatives, the gradient, the orthogonality of the gradient to level surfaces, the chain rule, critical points (the necessity of the vanishing of the first order derivatives and examples of saddle points). Integration in 2 variables, repeated integrals and changing the integration order, the dependence of the boundaries of the integrals on the order of integration. Optimization with Lagrange multipliers, examples and less proofs. Depending on time: the Euler Lagrange equation (in Variational Calculus).