Mathematics I

Numbers (real numbers; complex numbers). Fundamentals of functions with one variable (basic concepts, calculations using functions, bijective function inversions, overview of elementary functions; continuous functions, limits). Derivatives (definition of a derivative and the derivatives of elementary functions, rules for derivations, the geometric meaning of a derivative, rising and falling functions, convexity/concavity, stationary points and their classification; using derivatives, differential functions). Integrals (table of indefinite integrals, techniques of integration: introducing a new variable, the per-partes method; integrals of certain rational functions; the definition of a definite integral, using definite integrals for calculating the corresponding areas of curvilinear shapes and the volume/surfaces of rotational shapes, improper integral).