D1. Knowledge and understanding

To know the basic theory of: linear algebra, differential and integral calculus in several variables, ordinary differential equations, curves, surfaces.

D2. Applying knowledge and understanding

To be able to work with vectors and matrices, study the character of critical points, solve ordinary differential equations of some special classes, compute multiple and line integrals.

D3. Making judgements.

To be able to recognise the mathematical topics learned during the course in the framework of physical and chemical sciences and recognise contexts and problems in which the learned methods can be applied.

D4. Communication skills.

To be able to use correctly the basic mathematical formalism and illustrate definitions and statements in the correct form.

D5. Learning skills.

To be able to merge autonomously listening of lessons, study of the lecture notes and of possible other texts.

Differential and integral calculus for functions in one variable.
It is necessary to have passed the exam of Matematica I con esercitazioni before presenting to the oral test of Matematica II.

Linear algebra: vector spaces, linear mappings and matrices, determinants, scalar product and vector product. Topological properties of euclidean spaces: norm, distance, open and closed sets. Calculus for functions of several variables. Continuous functions. Partial and directional derivatives, gradient, tangent plane and level sets. Schwarz theorem. Optimization problems. Differential equations. Methods of integration for first order differential equations. Linear differential equations with constant coefficients. Multiple integrals. Double and triple integrals over simple domains. Reduction theorem. Change of variables. Curves: basic notions. Line integrals with respect to arc length and line integrals. Surfaces: basic notions. Conservative fields. Gradient, curl and divergence. Divergence theorem. Gauss-Green formulas. Stokes formula.

1. R. Adams, Calcolo differenziale 2, funzioni di più variabili. Casa Editrice Ambrosiana, Milano, 2000. 2. G. Anichini, G. Conti, Calcolo 1,2,3, Pitagora, Bologna. 3. N. Fusco, P. Marcellini, C. Sbordone. Analisi Matematica due, Liguori Editore, Napoli, 1996. 4. P. Marcellini, C. Sbordone. Calcolo, Liguori Editore, Napoli, 1993. 5. P. Marcellini, C. Sbordone. Esercitazioni di matematica, I vol. parte prima, Liguori Editore, Napoli, 1993. 6. P. Marcellini, C. Sbordone. Esercitazioni di matematica, II vol. parte prima e parte seconda, Liguori Editore, Napoli, 1993.

Linear algebra: vectors and matrices, linear mappings and matrices. Eigenvalues and eigenvectors. Calculus for functions of several variables. Basic topology in Euclidean spaces: distance, norm and scalar product, open and closed sets. Continuous functions. Partial and directional derivatives, gradient, tangent plane and level sets. Schwarz theorem. Local and global extrema. Differential equations. Methods of integration for first order differential equations. Linear differential equations with constant coefficients. Multiple integrals. Double and triple integrals over simple domains. Change of variables. Applications. Curves: basic notions. Line integrals with respect to arc length and line integrals of differential forms. Surfaces: basic notions. Conservative fields. Gradient, curl and divergence. Divergence theorem. Gauss-Green formulas. Stokes formula.

Frontal lessons at the blackboard expaining the theory and presenting a
consistent number of exercises. Student are strongly recommended to
actively take part to the lessons, especially in solving exercises.

For didactic materials, results of written examinations and other didactic informations see the website of the course on http://moodle2.units.it/

The program coincides with the topics treated in the lessons. The written test consists in solving exercises similar to those solved during the lectures. Caluculators may be used. Lecture notes can be consulted. A score not less than 15/30 gives access to the oral test up to the end of the september session. Any written test substitutes a possible preceding one. Oral test consists in verifying the comprehension of the contents and ability in explaining the subject. The final score depends on both written and oral tests.