( english version )

Mathematical analysis AB ( 9 CFU ) Finalità

The course provides the basic notion of calculus

Programma

Elementary algebraic properties of the real numbers (standard types of

equations and inequations); maximum and supremum of a set or a function;

algebraic properties and n-th roots of the complex numbers.

Graphs of the elementary fonctions and geometric transformations of the

same; properties of continuous functions (including mean value, existence of

a maximum, lipschitz continuity); limits of functions and of sequences of

real numbers; infinitesimals.

Properties of differentiable functions (including Rolle, Lagrange, Hopital

theorems); Taylor expansion (with Peano and Lagrange remainder); graphing a

function.

Indefinite and definite integral: definition and computation

(straightforward, by parts, by change of variables); integral mean and

fundamental theorems; Torricelli theorem; generalised integrals: definition

and comparison principles.

Numerical series: definition, convergence criteria, Leibniz and integral

criteria.

equations and inequations); maximum and supremum of a set or a function;

algebraic properties and n-th roots of the complex numbers.

Graphs of the elementary fonctions and geometric transformations of the

same; properties of continuous functions (including mean value, existence of

a maximum, lipschitz continuity); limits of functions and of sequences of

real numbers; infinitesimals.

Properties of differentiable functions (including Rolle, Lagrange, Hopital

theorems); Taylor expansion (with Peano and Lagrange remainder); graphing a

function.

Indefinite and definite integral: definition and computation

(straightforward, by parts, by change of variables); integral mean and

fundamental theorems; Torricelli theorem; generalised integrals: definition

and comparison principles.

Numerical series: definition, convergence criteria, Leibniz and integral

criteria.

Attività d'esercitazione

In smaller groups of students.

Modalità d'esame

The cross-examination consists in a written text divided into two parts (durino the same day) followed by a colloquium.

Propedeuticità

Prerequisites are basic facts on theory of sets, functions, trigonometry, analytic geometry.

Testi consigliati

E. Acerbi - G. Buttazzo: Analisi Matematica ABC vol.1, Pitagora, Bologna, 2003;

D. Mucci: Analisi Matematica - Esercizi 1, Pitagora, Bologna, 2004.

D. Mucci: Analisi Matematica - Esercizi 1, Pitagora, Bologna, 2004.