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