Fusco - Marcellini - Sbordone, Elementi di Analisi Matematica 2 ed. Liguori
Marcellini - Sbordone, Esercitazioni di Matematica – 2. First and second book. ed. Liguori
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.
Analysis I and Linear Algebra
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
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Training sessions: training of the students to modelling and solving a wide selection of problems in Calculus II. The training sessions are conducted so to:
-- help the students develop communication skills and apply the theoretical knowledge;
-- encourage independent judgement in the students.
Moodle learning platform: online teacher-student interaction, posting of additional notes, weekly exercise sheets, copies of past tests.
Remark: The suggested reading includes supplementary material that may be useful for further personal studies in Computer Science or in any scientific subject.
by appointment. A weakly meeting will be fixed according to the student's needs.
Dipartimento di Matematica ed Informatica(DIMAI)
Viale Morgagni, 67 I 50134 Florence, Italy
Type of Assessment
Intermediate and final written examination: A selection of exercises is proposed. The tests 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 skills, critical thinking and appropriate use of mathematical language.
• 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)
• Line Integration
• Double integrals
• Implicit functionTheorem