I. To acquire a good knowledge of the theory for series and sequences of functions in R.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
II. To develop and acquire the methods in the theory of continuous and regular functions in several real variables.
scheda docente
materiale didattico
Fruizione: 20402076 AM210 - ANALISI MATEMATICA 3 in Matematica L-35 R N0 PROCESI MICHELA, CORSI LIVIA
Programma
the course is used by AM210-Mathematical Analysis 3 offered by the Degree Course in Mathematics; See the course description on the page of the parent course: https://www.uniroma3.it/corsi/dipartimento-di-matematica-e-fisica/l/2025-2026/matematica-0580706203500001/, under "Course List"Testi Adottati
the course is used by AM210-Mathematical Analysis 3 offered by the Degree Course in Mathematics; See the course description on the page of the parent course: https://www.uniroma3.it/corsi/dipartimento-di-matematica-e-fisica/l/2025-2026/matematica-0580706203500001/, under "Course List"Modalità Frequenza
the course is used by AM210-Mathematical Analysis 3 offered by the Degree Course in Mathematics; See the course description on the page of the parent course: https://www.uniroma3.it/corsi/dipartimento-di-matematica-e-fisica/l/2025-2026/matematica-0580706203500001/, under "Course List"Modalità Valutazione
the course is used by AM210-Mathematical Analysis 3 offered by the Degree Course in Mathematics; See the course description on the page of the parent course: https://www.uniroma3.it/corsi/dipartimento-di-matematica-e-fisica/l/2025-2026/matematica-0580706203500001/, under "Course List"
scheda docente
materiale didattico
Fundamentals of topology in R^n. Functions of several variables: limits and continuity. Open, closed, connected, and compact sets. Functions of several variables: differentiability, C^k functions, definition of the tensor of p-th order derivatives. Taylor's formula with integral, Lagrange, and Peano remainder terms. Local maxima and minima. Implicit function theorem. Method of Lagrange multipliers.
Fruizione: 20402076 AM210 - ANALISI MATEMATICA 3 in Matematica L-35 R N0 PROCESI MICHELA, CORSI LIVIA
Programma
Sequences and series of functions: pointwise, uniform, and total convergence; passing to the limit under the integral and derivative signs; criteria for uniform convergence. Matrix exponential. Fourier series: basic definitions, Bessel's inequality, Riemann-Lebesgue lemma. Pointwise convergence of Fourier series for piecewise smooth functions.Fundamentals of topology in R^n. Functions of several variables: limits and continuity. Open, closed, connected, and compact sets. Functions of several variables: differentiability, C^k functions, definition of the tensor of p-th order derivatives. Taylor's formula with integral, Lagrange, and Peano remainder terms. Local maxima and minima. Implicit function theorem. Method of Lagrange multipliers.
Testi Adottati
Analisi Matematica II, Giusti - Analisi Matematica II, ChierchiaModalità Frequenza
attendance is not compulsory but suggestedModalità Valutazione
The exam consists of a written test (which can be replaced by passing two mid-term tests) covering the course topics, and an oral exam.