Università Roma Tre

Numerical sets (N, Z, Q and R), axiomatic construction of R, construction of N and principle of induction, complex numbers; elements of topology in R and Bolzano-Weierstrass theorem; real functions of real variable, limits of functions and their properties, limits of sequences, notable limits, the Napier number; continuous functions and their properties; derivative of functions and their properties, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), convex / concave functions; function graph; Riemann integration and properties, integrability of continuous functions, fundamental theorem of integral calculus, integration by substitution and by parts, integration rules; numerical series, simple and absolute convergence, convergence criteria for series with positive terms and for series with any terms; Taylor series; improper integrals.

Analisi matematica I Marcellini-Sbordone
Analisi matematica I Pagani-Salsa
Esercitazioni di Matematica Marcellini-Sbordone