Teacher

prof.ssa aggr. Giuseppina Gerarda BARBIERI

Credits

6 CFU

Language

Italian

Objectives

The course provides the inecessary mathematical methods for the engineering applications by the study of differential and integral calculus.

Acquired skills

- Acquisition of the concept of limit and continuity for multiple variable functions.
- To be able to correctly solve free and constrained optimization problems.
- To be able to handle with the properties of implicit functions.
- Knowledge of multiple integrals and of integration methods.
- Knowledge of vector fields and their integral and differential relations.

Lectures and exercises (topics and specific content)

Foundations of functional analysis: metric spaces; contractions and fixed point theorems; normed spaces and Banach spaces; Hilbert spaces (8 hours).
Differential calculus and optimization: limits, continuity, differentiability, derivative with respect to a vector, gradient; higher order derivatives and Taylor formula, free extrema; implicit function theorem and consequences, local invertibility, constrained extrema (26 hours).
Integral calculus: Lebesgue measure and integration, multiple integrals and reduction theorems, change of variables, line and surface integrals (14 hours).
Differential forms: exact forms, the Gauss-Green theorem, Stokes theorem (12 hours).
Exercises (20 hours).

References

- Canuto, Tabacco, Analisi Matematica II, Ed. Springer, 2008
- Salsa, Squellati, Esercizi di Analisi matematica 2, Ed. Zanichelli, 2011
- Giusti, Analisi Matematica 2, Bollati Boringhieri

Type of exam

Written and oral

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