Module page
Analisi matematica II
| academic year: | 2013/2014 |
| instructor: | Italo Capuzzo Dolcetta |
| degree course: | Mathematics - DM 270/04 (triennale) |
| type of training activity: | caratterizzante |
| credits: | 9 (72 class hours) |
| scientific sector: | MAT/05 Analisi Matematica |
| structure: | annuale semestralizzato |
| teaching language: | italiano |
| program: | A-H |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject:
DETTAGLI in INGLESE
- Differential calculus in several variables: limits and continuity, derivatives, differentials, tangent plane, higher order derivatives, Taylor's formula. Determination of relative maxima and minima and absolute ones.
- Vector-valued functions, inverse function theorem and Dini theorem.
- Constrained maxima and minima and the Lagrange multipliers method.
- Curves and surfaces, curve length and surface area.
- Differential forms and integrability conditions.
- Integration for functions of several variables: Riemann integral, extended integrals and an outline of Lebesgue integral, Fubini theorem, derivative under the integral sign, change of variables.
Suggested reading:
C.D.Pagani, S. Salsa: Analisi Matematica Volume 1 e Volume 2, Zanichelli
N. Fusco, P. Marcellini, C. Sbordone: Analisi Matematica due Liguori Ed.,
Type of course: standard
Exercises:
- In allegato alcuni esercizi e problemI su FUNZIONI 1.
- FUNZIONI.0
- FUNZIONI. 1
- CURVE
- FUNZIONI.3
- FUNZIONI.2
Useful links:
- www1.mat.uniroma1.it/people/birindelli/esercizi/registrazioniex/richiestAn2.cgi
- Risultati della prova scritta di meta' corso in allegato
Knowledge and understanding:
Students who pass the final examination will have a thorough knowledge of the main concepts of calculus for functions of several variables, with particular attention to the theory of metric and normed spaces, ordinary differential equations, differential calculus in several variables, complex analysis and integration for functions of several variables.
Skills and attributes:
Students who pass the final examination will be able to apply techniques of multivariate calculus. In particular will be able to solve some classes of ordinary differential equations, compute integrals of functions of two and three variables, and apply the techniques of calculius to the solution of several problems.
Personal study: the percentage of personal study required by this course is the 65% of the total.