Matematica | MATHEMATICAL ANALYSIS IV

cod. 0512300011

MATHEMATICAL ANALYSIS IV

	0512300011
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2015/2016

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2010
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	7	56	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	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.

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 SEVERAL REAL VARIABLE: CONTINUITY, DIFFERENTIABILITY.

	Contents
	MULTIPLE INTEGRALS. RECTIFIABLE CURVES. DIFFERENTIAL FORMS, STOKES FORMULA. DIVERGENCE THEOREM, GAUSS-GREEN FORMULA. DINI THEOREM, LAGRANGE MULTIPLIERS. INVERSION THEOREM.

	Teaching Methods
	FRONTAL LESSONS. PRACTICE LESSONS.

	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