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.

Limits and continuity
Neighborhood of a point. Definition of continuity and limit of a function: basic properties. Sequences of real numbers. Uniform continuity.

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

Series of real numbers
Definitions and convergence criteria.

Riemann Integral
Definition of Riemann integral. Fondamental theorems of calculus. Integration by parts and substitution. Integration of rational functions.

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