Sequences and series of functions: pointwise and uniform convergence. Power series: the domain and the radius of convergence. Abel's theorem. Taylor's series. Functionals spaces connected with the uniform convergence. A fixed point theorem. Implicit functions: Dini's theorem in the scalar and vector cases. The inverse function theorem. Constrained optimization. First order differential equations: the Cauchy problem, existence and uniqueness of solutions. Differential equations of higher order. Linear equations. Curves in R^n: length, integration along curves. Differential forms, exactness and related results. Curves and differential forms. Conservative fields. Closed and exact forms. Potentials.