The aim of the course is to illustrate the basics of differential and integral calculus for functions of several variables, of the theory of numerical series and series of functions and of ordinary differential equations, as well as to introduce students to modeling and solving simple problems of applicative interest that make use of the mathematical tools developed. At the end of the course the student will know the fundamental results and will be able to understand the proofs of the main theorems (D1), will use the knowledge acquired to solve simple problems and exercises (D2), will recognize the situations and problems in which the learned techniques can be advantageously used (D3), will be able to express appropriately (D4) and to consult elementary texts on course topics (D5).

Differential and integral calculus in one variable. Linear algebra and analytic geometry.

Metric spaces and geometry of R ^ N. Functions between metric spaces. Continuous functions. Limits. Sequences in a metric space. Numerical series and series of functions. Developability of a function as a power series and Taylor polynomial. Differential calculus in R ^ N. Problems of free and constrained maximum and minimum. Integral calculus in R ^ N. Line and surface integrals. Vector fields. Differential operators: gradient, curl, divergence, Laplacian. The divergence and curl theorems (Gauss-Green and Kelvin-Stokes). Differential equations.

P. Omari, M. Trombetta, Appunti del corso di analisi matematica 2 (per il diploma universitario), Università degli Studi di Trieste, Facoltà di Ingegneria. (Ask the teacher). V. Barutello, M. Conti. D. Ferrario, S. Terracini, G. Verzini, Analisi matematica (con elementi di geometria e calcolo vettoriale) Volume 2, Apogeo.

The detailed program can be found in the site http://www.dmi.units.it/~obersnel/

Frontal lessons and exercises. Active involvement of the students. Homework available on the web site. Group exercises and activities.

See http://www.dmi.units.it/~obersnel/ More information is available on the Moodle website of the course. The teacher can be contacted by email at obersnel@units.it

The exam consists of two tests: an exercises and a theory exam. The first test is written and asks for the resolution of some simple exercises on the model of what was done in class and in practice sessions, some of which may however require reasoning autonomy. The theory test is aimed at verifying the theoretical knowledge of the discipline (definitions, statements and proofs of theorems) and the students' communication skills; it can possibly consist of a written part but always ends with an oral interview. To qualify for the theory test, students must obtain a minimum score of 15/32 in the exercise test. Both tests contribute equally to the final grade, which is in any case awarded by an overall assessment and is not simply the result of an average