Portale di Ateneo - En.Unibs.it

Notions of formal logic and theory of sets

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.

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

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. Convex functions.