( english version )
Mathematical analysis AB ( 9 CFU )
Prof. Domenico Mucci
     Tel. 0521 906959 - Fax. 0521 906950           E-mail. domenico.mucci@unipr.it

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.

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.

 
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