SECS-S/06 - 9 CFU - 1° Semester

1st MODULE Number of credits : 3 CFU

Program description

ELEMENTS OF MATHEMATICAL LOGIC: languages and propositions; connectives; quantifiers. SET THEORY: properties, subsets, operations. Functions. Binary relations. Real numbers and inequalities. Basics of trigonometry.

COMBINATORICS: dispositions, combinations and permutations. Binomial theorem, binomial coefficients. ANALYTICAL GEOMETRY: Cartesian coordinate system. Straight line equation in the plane.

MATRICES AND DETERMINANTS: definitions and classifications. Sum and product between matrices. Inverse matrix. Determinant and its property. Rank of matrix

LINEAR SYSTEMS: dependence between linear forms. Definitions and properties. Normal linear systems: Cramer’s rule. Rouché-Capelli Theorem. Gaussian elimination and solution of parameterized systems. Applications to economic problems.

2nd MODULE Number of credits: 3 CFU

Program description

REAL FUNCTIONS OF REAL VARIABLE: definitions, classifications, geometrical representation. Composite functions and inverse functions. Limits: definitions and theorems. Continuous functions. Infinitesimals and infinities.

DERIVATIVES AND DIFFERENTIALS: definitions, properties and their geometric interpretation. Derivatives of elementary functions. Derivatives and differentials of sum, product and quotient of functions. Derivatives of composite and inverse functions. Derivatives and differentials of n-th order. Main theorems on differentiable functions.

APPLICATIONS OF DIFFERENTIAL CALCULUS: Taylor’s and Mac Laurin’s formulas. Indeterminate forms. Monotonic functions, convex functions, local and global extrema, inflection points, asymptotes. Elasticity of a function. Study of function. Applications to economic problems. INTEGRALS: indefinite integral and primitives. Definite integral and its geometric interpretation. Main methods of integration.

3rd MODULE Number of credits : 3 CFU

Program description

INTEGRALS: indefinite integral and primitives. Definite integral and its geometric interpretation. Main methods of integration.

ANALYTICAL GEOMETRY: Conics: circle, ellipse, parabola, hyperbola.

Salvatore Greco, Benedetto Matarazzo, Salvatore Milici, Matematica Generale, Giappichelli Editore, Torino, 2010.