MATHEMATICAL ANALYSIS II

The course aims to provide the basic knowledge of differential and integral calculus for several variables functions and the ODE's theory . Students will be able to apply the mathematical tools to some problems arysing from Physics.

In particular the course objectives are:

Knowledge and understanding:students will learn the differential calculus for functions of more real variables and its applications to optimization problems, the theory and the resolutive methods for some ordinary differential equations, the integral calculus on domains, curves and surfaces.

Applying knowledge and understanding: by means of examples related to applied sciences, students will focus on the central role of Mathematics within science and not only as an abstract topic. Furthermore, they will be able to apply the mathematical tools to some problems arysing from Physics.

Making judgements: students will be stimulated, individually or in groups, to work on specific topics they have not studied during the class, developing exercises related on the field knowledge with greater independence. Seminars and lectures are scheduled to give students the chance to illustrate guided exercise on specific topics in order to share them with the other students and to find together the right solutions.

Communication skills: studying Mathematics and dedicating time to guided exercise and seminars, students will learn to communicate with clarity and rigour both, in the oral and written analysis. Moreover, students will learn that using a properly structured language means to find the key to a clear scientific and non-scientific communication.

Learning skills: students, in particular the more willing one, will be stimulated to examine in depth some topics, thanks to individual activities or working in group.

The principal concepts and learning outcomes will be structured by planning frontal lectures. Furthermore, to improve the making judgements and communication skills, students will dedicate time to guided exercises (e.g. multiple choice) and they can work in groups or individually .

The course is organized by lectures. There will be some team practices, during which students can work in groups or individually. Students will also participate in seminar discussions, developing exercises related on the field knowledge.

Sequences and series of functions. Power series. Expansion of given functions in power series.

Functions of several variables: Continuity and differentation. Local and global extrema. Implicit functions.

Multiple integrals. Curves and surfaces. Differential forms. Conservative vector fields. ODE. Linear ODE.

1. G. Fiorito, Analisi Matematica 2, Spazio Libri

2.N.Fusco, P.Marcellini, C.Sbordone, Analisi Matematica 2, Liguori

3. C.Pagani, S.Salsa, Analisi Matematica 2, Zanichelli

4. M.Bramanti, Esercitazioni di Analisi Matematica 2, Esculapio
5. P.Marcellini, C.Sbordone, Esercitazioni di Matematica, Vol.2, Parte I e II, Zanichelli.