Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Differential and integral calculus for one-variable functions; linear algebra.

The aim of the course is that of providing further mathematical tools commonly employed in the engineering sciences, by means of introducing the basic elements of the differential and integral calculus for real functions of several variables and of the ordinary differential equations.

The many applications of the course topics in the applied sciences, for example in chemistry and in physics, will provide the student with the ability of modeling and solving practical engineering problems; they will also increase the ability of choosing independently the best solution techniques. The course will also provide the student with the ability to use mathematical laws in general scientific problems.

The expertise acquired in this course will be needed in order to study the material of later courses. Individual and collective problem-solving sessions will improve the ability to develop independent thought and learning capabilities. Oral presentations of the topics taught in the course, with the language proper of the basic disciplines of the degree course will help developing communication skills.

Linear differential equations and equations with separable variables. Laplace transformations in the real field. More-variable functions: infinitesimal and differential calculus, maxima and minima. Curves and integrals over a curve. Multiple integrals. Gauss-Green formula in the plane and applications. Vector fields: conservative fields and potentials. Regular surfaces and integrals over a surface. Flux of a field through a surface. Differential operators: gradient, divergence, rotor. Functions of a complex variable, olomorphic functions and Cauchy-Riemann conditions, analitic functions ad their properties. Integrals of complex functions, Cauchy integral formula. Laurent series, classification of the singularities of an analitic function. Theorem of residues.

The student will be assessed through on a written test and an oral test. The written test will assess the ability to solve problems by using the learned techniques. The oral test will assess the learning of the theory and the exposition skills.

In the exams the student have to prove that he understands the concepts presented in the course, that he knows the results and methods presented in the lectures, and finally that he is able to set a problem and solve it properly through the learned methods.

In the written test is evaluated the ability to set up and properly solve the posed problems, using their own methods of the course. In the oral exam it is assessed the knowledge of the concepts and results presented in the lectures, the presentation skills and the ability to make connections between the various concepts introduced.

For each of the tests indicated above it is assigned a score between zero and thirty. The student will be admitted to the oral exam only if he passed the written test. The highest rating, equal to thirty of thirty, is achieved by demonstrating in-depth knowledge of the course contents and full autonomy in the performing the test. The minimum assessment, equal to eighteen of thirty, is assigned to students who manage to solve the proposed problems and who demonstrate sufficient knowledge of the topics of matter.The overall grade, out of thirty, is derived from the comparative evaluation of both tests. The praise is reserved to the students who, having carried out the tests correctly and completely, has shown a special independence and excellence.

Hass - Weir - Thomas, Analisi Matematica 2- Pearson P. Marcellini - C. Sbordone, Analisi Matematica 2- Liguori Barozzi, Matematica per l'ingegneria dell'informazione- Zanichelli

- Ingegneria Biomedica (Corso di Laurea Triennale (DM 270/04))
- Ingegneria Elettronica (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427