Mathematical Analysis II - 1st module (the English translation of "Analisi matematica II - 1° modulo")
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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