Numbers and Sets
Equations and Inequalities (restricted to first and second order or traceable to first and second order)
Basic functions (Main elementary functions: graphs and geometric and analytical properties: sign function, identical function, linear and affine function, absolute value function, power function, root function and their analytical properties, power function with real exponent and its analytical properties, exponential function and its analytical properties, logarithm function and its analytical properties, logarithmic calculation, exponential and logarithmic equations and inequalities, circular functions and their inverse)

Tools for the applications (Straight line equation, sequences, sequence limits, function limits, derivative and their algebra)
Applications to the differential calculus (polinomial and rational functions' graphs, linar approximations)
Integral calculus.
Introduction: intuitive integral concept and some historical notions, link with differential equations. Defined integral: integral as an area measure, subdivision of an interval, rectangles, finer subdivisions, lower integral (upper) sum, lemma on the inequality between lower and upper sums related to different subdivisions, corollary on the inequality between lower and upper extreme of integral sums, integrable function according to Riemann, the Dirichlet function, Riemann characterization theorem, homogeneity proposition of the integral, monotonic proposition of the absolute value, additivity proposition with respect to the integration interval, additivity proposition with respect to the integrated functions, proposition of non-negativity, proposition of monotony, the integral mean theorem, mean value of a function.
Indefinite integral: integral function, Torricelli-Barrow theorem, primitive function, proposition two primitives differ in a constant, indefinite integral, corollary fundamental formula of integral calculus.
Integration methods: some fundamental primitives, calculation of immediate integrals, proposition of integration by parts, finite factor, differential factor, proposition of integration by substitution, calculation of definite integrals.
Integration of fractional rational functions: proper and improper rational functions, division between polynomials, integration rules for second degree denominator (cases Δ> 0, Δ = 0, Δ <0).
Differential equations
Introduction: general (order, solution, integral curves).
Geometric interpretation of solutions: simple differential equations, directional fields, Cauchy problem.
Linear equations of the first order: proposition of existence of the solution (with proof), proposition of existence and uniqueness of the Cauchy problem (with proof). Numerical examples.
A microeconomic model of market dynamics: the equilibrium price.
Particular cases of first order linear equations: proposition of existence and uniqueness of the Cauchy problem relating to the first degree homogeneous linear differential equation (with proof). Numerical examples.
Separable variable equations: proposition of the implicit solution to the Cauchy problem relating to a differential equation with separable variables (with proof). Numerical examples.
Population dynamics models: the Malthus model and the Verhulst logistic model.