Classrooom-taught lessons including also exercising sessions during which it will be shown how to apply the theoretical concepts introduced during the course.
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.
MATRICES AND DETERMINANTS: definitions and classifications. Sum and product between matrices. Inverse matrix. Determinant and its property. Rank of matrix.
LINEAR SYSTEMS: linear forms. Definitions and properties. Normal linear systems: Cramer’s rule. Rouché-Capelli Theorem. Solution of parameterized systems.
ANALYTICAL GEOMETRY: Cartesian coordinate system. Straight line equation in the plane.
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. Study of function. Elasticity of a function.
INTEGRALS: indefinite integral and primitives. Definite integral and its geometric interpretation. Main methods of integration.