Sequences of functions and power series
Ordinary differential equations
Maximum of functions of several variables
Implicit functions, curves and differential forms
Fusco - Marcellini - Sbordone, Elementi di Analisi Matematica 2 ed. Liguori
Marcellini - Sbordone, Esercitazioni di Matematica – 2. First and second book. ed. Liguori
Learning Objectives
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.
Prerequisites
Analysis I and Linear Algebra
Teaching Methods
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
Further information
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
Type of Assessment
The exam is written and oral and consists of:
- in a written exam of 3 hours without the aid of notes or books. The written test consists of 3-4 of skill application exercises. The exercises involve similar problems to those carried out in class.
- In a technical conversation of about an hour with the teacher on concepts and theorems related to sequences of functions and power series, ordinary differential equations, maximum of functions of several variables, implicit functions, curves and differential forms in order to bring out the knowledge acquired on the subject
The aim of this analytical graduation performance of the student is to reliably assess the level of achievement of the expected learning outcomes described above.
Course program
• 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