B006808 - REAL ANALYSIS II

Italian

The course aims at providing students with a thorough understanding of the scientific principles underlying the study of functions of several variables and linear ordinary differential equations

Acquired skills.
At the end of the course, the student should be capable of solving ordinary differential equations and of studying the behaviour of functions of several variables.

• Sequences and series of functions Power series
• Fourier series
• Functions of several variables
• Limits of functions of several variables
• Partial derivatives and differentiability
• Theorems on the differentiability of the functions and Schwartz Theorem
• Maxima and minima of functions of several variables
• Lagrange multiplier
• Ordinary differential equations of the first order
• Cauchy Theorem
• Linear differential equations of the second order
• Resolution of certain types of equations (separation of variables, linear equations with constant coefficients, method of variation of constants)
• Curves
• Line Integration
• Exact and closed differential forms
• Double integrals
• Implicit functionTheorem

Analysis I and Linear Algebra

Total number of hours of the course: 150

Number of hours for personal study and other individual learning: 98

Number of hours for classroom activities: 48

Written and oral examination on the course topics.

• Sequences and series of functions Power series
• Fourier series
• Functions of several variables
• Limits of functions of several variables
• Partial derivatives and differentiability
• Theorems on the differentiability of the functions and Schwartz Theorem
• Maxima and minima of functions of several variables
• Lagrange multiplier
• Ordinary differential equations of the first order
• Cauchy Theorem
• Linear differential equations of the second order
• Wronskian Theorem
• •Resolution of certain types of equations (separation of variables, linear equations with constant coefficients, method of variation of constants)
• Curves
• Line Integration
• Exact and closed differential forms
• Double integrals
• Implicit functionTheorem

Fusco - Marcellini - Sbordone, Elementi di Analisi Matematica 2 ed. Liguori
Marcellini - Sbordone, Esercitazioni di Matematica – 2. First and second book. ed. Liguori

Office hours:
by appointment.

Dipartimento di Matematica ed Informatica(DIMAI)
Viale Morgagni, 67 I 50134 Florence, Italy
Tel: +39 055 2751405
Fax: +39 055 2751413
e-mail: vincenzo.vespri@unifi.it