Matematica | MATHEMATICAL ANALYSIS III

cod. 0512300008

MATHEMATICAL ANALYSIS III

	0512300008
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2013/2014

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO

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

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
MAT/05	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
MAT/05	2	24	EXERCISES	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	Objectives
	AWARENESS:IN THIS COURSE ARE INTRODUCED THE BASIC PORPERTIES OF DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES. MAIN ATTENTION IS FOCUSED ON OPTIMIZATION PROBLEMS. THE BASIC TECHNIQUE FOR SOLVING ELEMENTARY ORDINARY DIFFERENTIAL EQUATIONS ARE GIVEN 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 DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES. MAIN ATTENTION IS FOCUSED ON OPTIMIZATION PROBLEMS. THE BASIC TECHNIQUE FOR SOLVING ELEMENTARY ORDINARY DIFFERENTIAL EQUATIONS ARE GIVEN
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
	DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES, TANGENT PLANE, MAX AND MIN, TAYLOR FORMULA. SEQUENCE OF FUNCTIONS, SERIES OF FUNCTIONS, POWER SERIES, TAYLOR SERIES, FOURIER SERIES. ORDINARY DIFFERENTIAL EQUATIONS, EXISTENCE AND UNIQUENESS OF SOLUTIONS, CAUCHY PROBLEM, EXACT SOLUTIONS, QUALITATIVE ANALYSIS.

	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