( english version )
Mathematical Analysis AB ( 9 CFU )
Prof. Giuseppe Rosario Mingione
     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.





 
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