Mathematics 1

Numbers (real numbers; complex numbers).
Basics of real functions (basic notions, operations between functions, inverse, outline of elementary functions, continuity, limits).
Derivative (definition of a derivative and derivatives of elementary functions, derivative rules, geometrical meaning of a derivative, increasing/decreasing of functions, convexity/concavity, stationary points and their classification; application of the derivative, differential of a function).
Integrals (table of indefinite integrals, different integration technics: new variable, per-partes; integration of rational functions; definition of definite integral, applications: area, volume, length, improper integral).