Development of the subjects given in Mathematical Analysis 1: higher order derivatives, more on several variables.
ODEs, complements.
Sequences and series of functions.
Linear differential forms.

Lectures at the blackboard.

Oral examination.

Basics on Mathematical Analysis and Linear Algebra.

Global properties of continuous functions, higher order derivatives and more on several variables.

ODEs.

Sequences and series of functions.

Linear differential forms.



Global properties of continuous functions: maxima and minima, uniform continuity and applications (e.g., to integration theory).



Mean value theorems and their applications to functions of one or several variables (e.g., use of the sign of the derivatives, Taylor expansion, De L'Hopital's rule; differentiation of integrals depending on parameters; study of stationary points and convex functions in several variables, Lagrange multipliers).



Integral calculus in several variables (multiple, line and surface integrals; change of variables).



Basics on ODEs and systems (Cauchy problem, global and local solutions).

The easiest and basic elements on linear ODEs.



Uniform convergence and applications.

Power series in 1D.



Exact and closed linear differential forms in several variables.

G. Gilardi: "Analisi Matematica di Base", seconda edizione, McGraw-Hill, 2011.

Some material at http://www-dimat.unipv.it/gilardi/WEBGG/analisi2.htm