LINEAR ALGEBRA: Sets, number sets, functions; real line, cartesian plane. Vectors in R^n. Matrices. Rank. Gauss elimination. Determinant and applications. Scalar product. Lines, planes and circles. Linear systems: study and resolution. Change of coordinates. Linear applications. Diagonalization.
ANALYSIS: 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. Differential equations.