1) Metric spaces, complete metric spaces, sequentially compact sets and their properties, continuous functions. 2) Contraction theorem. 3) Normed spaces, linear operators between normed spaces. Equivalent norms. 4) Functions from R^n in R^m. Continuity and differentiability. Partial derivatives, gradient and Jacobian matrix. Sufficient condition for differentiability. Chain rule. 5) Mean value theorem. Functions with null differential on connected sets. 6) Second partial derivatives. 7) Taylor’s theorem in several variables. 8) Implicit functions. Local theorem of existence and uniqueness. 9) Maxima and minima. First order conditions. 10) Hessian matrix and sufficient conditions for extrema. 11) Extrema with constraints. The Lagrange multipliers method. 12) Peano measure in R^n and measurable sets. 13) Integration on rectangles. Iterated integrals. Riemann integral on measurable sets. 14) First order differential equations and systems. Solutions. 15) The local existence and uniqueness theorem for the Cauchy problem. 16) Maximal solutions. 17) Sufficient conditions for existence on a interval. 18) Differential Equations of order n. Linear equations of order n. Independent solutions and solution space. 19) Linear equations of order n with constant coefficients.