N. Fusco, P. Marcellini, C. Sbordone, Analisi Matematica due, Ed. Liguori 2005.
Marcellini - Sbordone, Esercitazioni di Matematica - 2 volume - parte prima e seconda ed. Liguori.
C. Pagani, S. Salsa, Analisi matematica 2, ed. Zanichelli 2015
Learning Objectives
The course aims to provide the students with fundamental knowledge and understanding in solving Ordinary Differential Equations and in studying the behaviour of functions of several variables. One of the aims is to let the students develop basic technical skills, and critical thinking, needed when modelling and solving mathematical problems in different settings. Special attention will be paid to help the students to develop communication skills necessary for teamwork. The course covers topics and provides learning skills that are needed, or strongly suggested, to pursue a degree in Computer Science or in any scientific subject.
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: 102
Number of hours for classroom activities: 48
Further information
Office hours:
by appointment. A weakly meeting will be fixed according to the student's needs.
Dipartimento di Matematica ed Informatica(DIMAI)
Viale Morgagni, 65 I 50134 Florence, Italy
e-mail: roberta.fabbri@unifi.it
Tel. 0552751469
Type of Assessment
Final written examination: A selection of exercises is proposed. The problems are designed to assess the ability of the students to apply their skills to problem modelling and solving. In the evaluation, special attention is paid to the correctness of the solution procedure, as well as to the originality and effectiveness of the methods adopted.
Oral examination: A number of questions are posed. The oral examination is designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication ability, critical thinking and appropriate use of mathematical language.
Course program
• 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
• Double integrals
• Change of variables for double integrals