italian version

Aims :

To impart the basic elements of differential and integral calculus for the functions of one real variable.

Topics :

Sets. Relations. Functions. Sets of numbers. The induction principle. Elements of combinatorial calculus. Elementary functions. Complex numbers.
Sequences of real numbers. Limits of sequences. Indefinite forms. Neper’s number and other relevant limits. Series. Geometric series and generalized harmonic series. Convergence criteria. Simple and absolute convergence. Leibnitz’s criterion. Limits and continuity of real functions. The theorems of Weierstrass and of the intermediate values. Continuity of elementary functions and their inverses. Infinitesimal quantities and their comparison. Derivatives. Differentiability of the elementary functions and their inverses. Derivatives of higher order. The theorems of Fermat, Rolle, Lagrange and Cauchy. Primitives. Convexity . The theorems of de l'Hospital. Taylor’s formula. Integrability and definite integrals. The fundamental theorem of integral calculus. Indefinite integrals, integration by sums, by parts and by substitution. Singular integrals, simple and absolute convergence. The comparison theorem and the criterion of the infinitesimals. Integral criterion for series.


Textbooks :

M.Bramanti, C.D.Pagani, S.Salsa, Matematica, calcolo infinitesimale e Algebra lineare, Zanichelli.
P. Marcellini, C. Sbordone, Elementi di Analisi Matematica I, Liguori Editore
S.Salsa, A. Squellati Esercizi di Matematica, calcolo infinitesimale e Algebra lineare, vol.1, Zanichelli.

Exam :

Written test followed by an oral test

Tutorial Session :

Wednesday 10-15 and by appointment