Teacher

prof.ssa Roberta MUSINA

Credits

6 CFU

Language

Italian

Objectives

The course deals with the foundations of Mathematical regarding differential and integral calculus for functions of several variables, differential equations and series of functions. In addition to providing computing techniques, the aim of the course is to provide the scientific mentality, that is needed to successfully apply mathematical tools in solving engineering problem.

Acquired skills

- Acquisition of the concept of limit and continuity for multiple variable functions.
- Acquisition of the concept of limit in metric spaces and correct use of passage to limits for function sequences and series.
- 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)

Metric spaces: metric spaces; linear spaces; normed spaces; Banach and Hilbert spaces; the contraction principle (6 hours).
Sequences and series of functions: series; power series; Fourier series (12 hours).
Differential calculus of functions of several variables: limits; continuity; differentiation; directional derivatives (20 hours).
Differential calculus of vector-valued functions: differentation; "Chain rule" for differentiation (4 hours).
Optimization: maxima and minima (6 hours).
Constrained optimization: the implicit function theorem; constrained optima and the method of Lagrange multipliers (6 hours).
Integration of functions of several variables: integration of functions of several variables; reduction formulas; change of variables (4 hours).
Curves: curves; length of a curve (2 hours).
Exercises (20 hours).
Labs (20 hours).

References

- N. Fusco, P. Marcellini, C. Sbordone - Elementi di Analisi Matematica Due - Liguori Ed.

Type of exam

Written and oral

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