Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

notions from the course of Mathematics I

At the end of the course, students will know about the several kinds of functions from R^n to R^m (with n,m=3). In particular, students will handle curves, surfaces, vector fields and functions of two or three real variables. Moreover, they will be able to compute derivatives and integrals related to such functions. Such knowledge (which completes that of Matematica I course) will allow students to model real situations.

At the end of the course, students will be able to: 1) understand how real situations can be modelled; 2) apply such mathematical models to describe real situations. In particular, they will be able to use vector fields, curves, surfaces and functions of two and three real variable to describe real objects and forecast future behaviour.

Students will develop their capabilities in analysis, synthesis and independent judgement. This will be favoured by exercises and models included in this course. Finally, all the activities in this course will help the development of abstract thinking in the students.

real functions of many real variables; partial derivatives, differentials and directional derivatives; Taylor's polynomies; extremi of a function in several variables; surface and space integrals; vector fields and properties; curves and surfaces; integral over curves and surfaces; differential operators; Gauss-Green's and Stokes' theorems; Laplace transform.

Written test followed by an oral test.In the written part, students will solve several exercises where they have to apply tecniques of the multivariable calculus. In the oral test, students will be asked about topics concerning multivariable calculus.

Students will show capability of applying such notions in different exercises. Moreover, students will know about the main topics of multivariable calculus and will show their understanding of applications within the contexts explained during the lessons. .

for the minimum standard, student is supposed to be able to apply calculus tecniques to standard exercises. for the maximum standard, student is supposed to master these tecniques and to apply them in an autonomous way.

The knowledge of the basic notions of the course is necessary together with the capability of applying such notions to standard exercises. Moreover, the student will show their understanding of the meaning of what he has learnt. For excellence levels, the propriety of the mathematical language and of the competence in using theoretical notions within new situations is required.

. Bramanti, C.D: Pagani, S. Salsa, Matematica, Zanichelli

- Ingegneria Gestionale (Corso di Laurea Triennale Fuori Sede (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

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