# Matematica | MATHEMATICAL ANALYSIS IV

## Matematica MATHEMATICAL ANALYSIS IV

 0512300011 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2010 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 5 40 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS MAT/05 2 24 EXERCISES COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 LUCA ESPOSITO T
Objectives
AWARENESS:IN THIS COURSE ARE INTRODUCED THE BASIC PORPERTIES OF MULTIPLE INTEGRALS. MAIN ATTENTION IS FOCUSED ON DIVERGENCE THEOREM AND GAUSS-GREEN FORMULA. DIFFERENTIAL FORMS, STOKES FORMULA AND OPTIMIZATION PROBLEMS USING LAGRANGE MULTIPLIERS ARE STUDIED.
ABILITY TO APPLY AWARENESS:
ONE OF THE MAIN PURPOSE OF THE COURSE IS TO ACHIEVE THE STUDENT TO SOLVE PROBLEMS USING THE TECHNICQUE
ASSIMILATED.
INDEPENDENCE IN JUDJEMENT:THE STUDENT IS GUIDED TO DEVELOP DISCRIMINANTING ABILITIES ABOUT THE SUBJECTS STUDIED.
COMUNICATIVE ABILITIES: THE STUDENT WILL BE ABLE TO ARTICULATE THE STATEMENTS AND THE PROOF OF THE THEOREM DEALED IN THE COURSE.
EDUCATIONAL SKILLS: THE STUDENT WILL ACQUIRE THE KNOWLEDGE OF MATEMATICAL TOOLS THAT ALLOW HIM TO HANDLE WITH MORE ADVANCED MATEMATOCAL TOPICS.
Prerequisites
BASIC PROPERTIES OF FUNCTIONS OF A REAL VARIABLE: CONTINUITY, DIFFERENTIABILITY, INTEGRATION.
Contents
MULTIPLE INTEGRALS. RECTIFIABLE CURVES. DIFFERENTIAL FORMS, STOKES FORMULA. DIVERGENCE THEOREM, GAUSS-GREEN FORMULA. DINI THEOREM, LAGRANGE MULTIPLIERS.
Teaching Methods
FRONTAL LESSON
PRACTICE LESSON
Verification of learning
THE STUDENT WILL TAKE THE FOLLOWING TESTS:
WRITTEN AND ORAL EXAMINATION CONCERNING THE TOPICS COVERED IN THE COURSE.
Texts
N. FUSCO - P. MARCELLINI - C. SBORDONE, ELEMENTI DI ANALISI MATEMATICA II, LIGUORI EDITORE.
N. FUSCO - P. MARCELLINI - C. SBORDONE, ANALISI MATEMATICA II, LIGUORI EDITORE.
E. GIUSTI, ANALISI MATEMATICA 2, BORINGHIERI EDITORE.
F. CONTI, CALCOLO, MCGRAW-HILL LIBRI ITALIA.
P. MARCELLINI - C. SBORDONE, ESERCITAZIONI DI ANALISI MATEMATICA, VOLUME II, PARTE PRIMA, LIGUORI EDITORE