Portale di Ateneo - En.Unibs.it

Notions of formal logic and set theory.

Real Numbers Axioms. Sup/inf of a set of real numbers. Natural,
relative and rational numbers. Functions of a real variable.

Complex numbers. Definition and first properties. Operations:
sum, product, powers, and roots.

Sequences of real numbers. Definition. Limits. Subsequences.
Cauchy sequences.

Series of real numbers Definitions and convergence criteria.

Limits and continuity. Neighborhood of a point. Definition of
continuity and limit of a function: basic properties.

Theory of Derivatives. Definition of derivative and first
properties. Rules of derivation. Fundamental theorems on
derivatives. Application to the study of functions.
Classification of critical points. Taylor's polynomial.

Riemann Integral. Definition of Riemann integral. Fundamental
theorems of calculus. Integration by parts and substitution.
Integration of rational functions. Improper integrals.

Differential equations. Resolution of certain types of ordinary
differential equations: separation of variables, linear
equation of first order, linear equation with
constant coefficients.