Real functions of a variable: elementary functions (exponential, logarithms, trigonomètriques). Derivation and integration of functions of a variable. Problems of optimisation. Real functions of several variables: domain, partial derivatives, contour curves directional derivatives and optimisation. Differential equations of first order: general solution, the problem of initial value, equations of separable variables, linear equations, examples of the dynamics of populations and of the chemical kinetics. Linear differential equations of second order to constant coefficients. Examples: the system too much - spring, electrical circuits. Vectorial spaces, systems of linear and matrix equations. Values and own vectors.