Modules | Area | Type | Hours | Teacher(s) | |
ISTITUZIONI DI MATEMATICA II + ESERCITAZIONI | MAT/05 | LEZIONI | 54 |
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The students who successfully complete the course are expected to acquire: mastery of the basic techniques of the Calculus in several variables (limits, continuity, partial derivatives, integrals, vector fields; applications to the study of the behaviour of functions, etc.); some very basic knowledge of finite group theory (groups of symmetry of a "molecule", basic of the theory of the matrix representations of a group); some applications.
In the written exam (3 hours) as well as in the periodic written tests, the student must solve in an appropriate way the majority of the given exercises; during the oral exam the student must be able to demonstrate his/her understanding of the main topics and methods given in the course.
Methods:
Delivery: face to face
Attendance: Advised
Learning activities:
Teaching methods:
Vector calculus, equations of lines, planes, curves and surfaces; curves; functions of several variables: limits, continuity, partial derivatives, the main theorems and their applications to the study of local maxima and minima, with or without constrains; line integrals, vector fields, work, conservative vector fields; multiple integrals, change of variables and methods of calculations; basic group theory, groups of symmetry, matrix representations of groups; something on irreducible representations and their characters; applications.
Recommended reading includes: Adams, Calcolo Differenziale 2. Other suggested reading: Fano, Istituzioni di Matematiche 2; O. Salvetti, M.Salvetti, Note di Matematica (per Chimici) (Teoria dei gruppi a Applicazioni).
Methods:
In the written exam (3 hours) as well as in the periodic written tests, the student must solve in an appropriate way the majority of the given exercises; during the oral exam the student must be able to demonstrate his/her understanding of the main topics and methods given in the course.