99621 - MATHEMATICAL ANALYSIS T-2

Conoscenze e abilità da conseguire

Through the course the student learns the basic results as well as the basic tools of advanced calculus. At the end of the course, he/she masters the notions of partial derivatives, differentiability and integrability for functions of several real variables. He/She will be able to apply this knowledge to the study of many problems posed by pure and applied sciences.

Contenuti

Introduction to functions in several variables: topology of R^n, euclidean scalar product, differential calculus, extrema of a function: min, max and saddle points, the tangent plane.

Riemann integral of a function: definition, integration on normal domains.

Curves in R^n, line integrals: the work of a vector field; closed and exact differential forms. Conservative vector fields.

Ordinary differential equations: linear differential equations of first and second order; the corresponding Cauchy problem.

Testi/Bibliografia

S.Lang "Calculus of several variables" Springer Verlag (III edition)

C.Canunto-A.Tabacco "Mathematical Analysis II" Springer

 

Metodi didattici

Theory and exercises

Modalità di verifica e valutazione dell'apprendimento

Written and oral exams

Strumenti a supporto della didattica

Blackboard, video and pc

Orario di ricevimento

Consulta il sito web di Marco Mughetti