Real line; max and min, sup and inf in R; raw properties of functions of a real variable (monotonicity, boundedness, convexity). Elementary functions, graphical representation and properties. Limits and continuity. Derivatives (definitions, theorems, calculus, global properties). Study of the graph of a function. Approximation (Taylor''''s theorem). Integrals: definition, theorems, methods of integration. Improper integrals. Introduction to differential equations and some cases of solution and qualitative analysis.