Integrals: Riemann integral, integrability, mean value theorem, fundamental theorem of calculus, primitive functions, integration by parts, integration by substitution, integration of some rational functions, improper integrals.
Ordinary differential equations: basic notions, first order equations (linear ones, with separable variables, in normal form, Cauchy problem), higher order equations (normal form, Cauchy problem, second order linear equations with constant coefficients).
Functions of several variables: elementary properties of Rn, limits, continuity, partial derivatives, gradient, differentiability, directional derivatives, higher order derivatives, hessian matrix, Taylor's polynomials, critical points, unconstrained local extremum points, saddle points, convex sets and functions, curves (basic notions, parametric equations, tangent vector, length), level curves, implicit functions, constrained local extremum points, Lagrange multipliers, global extrema of continuous functions with compact domain, double integrals.