( english version )

Mathematical Analysis AB ( 9 CFU ) Tel. 0521/032346 - Fax. 0521/032350 E-mail. giuseppe.mingione@unipr.it

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.

Differential equations: solution of first and second order linear differential equations with constant coefficients and some easy types of right hand side.

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.

Differential equations: solution of first and second order linear differential equations with constant coefficients and some easy types of right hand side.