Functions: Function, domain, image, graph. Bounded functions, injective, surjective and bijective functions. Composite function. Inverse function. Monotonicity theorem of a composite function. Even, odd functions. Exponential function and logarithmic function.
Concept of limit: Euclidean distance. Definition of limit (various cases). Uniqueness of the limit. Right and left limit. Sign theorem for limits. Comparison theorem. Local maxima and minima. Algebra of limits. forms of indecision. Limit of compound functions.
Horizontal, oblique and vertical asymptotes.
Continuous functions of one real variable: Definition of continuous function. Continuity from right and from left. Sign theorem for continuous functions. Composition of continuous functions. Classification of discontinuity points. Continuity of monotone functions. Theorem of zeros. Corollary to the zeros theorem. Intermediate value theorem. continue (no dim.). Continuity of the inverse function. Weierstrass theorem.
Differential calculus: Secant and tangent line. Difference quotient and derivative. Geometric meaning of the derivative. Derivatives of elementary functions (calculation through the definition of derivative). Differentiable functions are continuous. C1 functions. Right derivative and left derivative and their geometric meaning. Corner points and cusps. Algebra of derivatives. Derivative of a product, a quotient and a compound function. Derivative of the inverse function. Derivative of log(x), arcsin(x), arccos(x),arctan(x) . Derivative of log|x|, log|x|,ax . Fermat's theorem (dim.). Critical points. Finding the local extremum points of a function. Rolle's theorem (dim.). Lagrange mean value theorem (dim.). Monotonicity of a differentiable function and sign of the derivative. de l'Hopital's theorem. Corollary to de l'Hopital's theorem. Higher order derivatives. Convex functions and concave functions. Convex functions and continuity (without dim.). Geometric meaning of convexity. Convexity and sign of the second derivative. Inflection points. Vertical tangent flexures. Inflection points and second derivative. Study of functions.

Integrals: Definition of the Riemann integral. Partition of an interval. Upper sums and lower sums. Integrability of continuous and bounded functions. Relationship between the definite integral and the area of ​​the subgraph of an integrable function. Properties of the integral. Integral mean value theorem (dim.). Definition of integral function. Fundamental theorem of integral calculus (dim.). Definition of primitive. The primitives of a function differ by an additive constant. Calculation of the integral defined through one of its primitives (dim.). Indefinite integral. Primitives of elementary functions. Integration by parts. Integration by substitution. Integration of rational functions.
Linear algebra: linear systems, Rouché-Capelli theorem, Gauss elimination method. Vector spaces, linearly independent vectors. Bases.

Probability: Conditional probability, Bayes' Theorem, main distributions (Gaussian, Poisson, binomial, etc.)