Fisica | CALCULUS II

cod. 0512600002

CALCULUS II

	0512600002
	DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
	EQF6
	PHYSICS
	2017/2018

PERCORSO COMUNE Cohort 2016/2017

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	ANNUALE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	12	96	LESSONS	BASIC COMPULSORY SUBJECTS

PROFESSORS

	ANNA CANALE T Curriculum
	LUCA ESPOSITO Curriculum

	Objectives
	THE COURSE DEALS WITH FUNCTIONS OF SEVERAL VARIABLES, DIFFERENTIAL EQUATIONS, SEQUENCES AND SERIES OF FUNCTIONS. THE AIM IS TO REACH A GOOD LEVEL OF UNDERSTANDING AND KNOWLEDGE OF THE TOPICS AND TO BE ABLE TO APPLY THE METHODS AND RESULTS TO DIFFERENT AREAS, IN PARTICULAR TO THE PHYSICS.

	Prerequisites
	GOOD KNOWLEDGE OF THE SUBJECTS CONTAINED IN THE COURSE ANALISI MATEMATICA I.

	Contents
	PART I DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES. LINE INTEGRALS. DIFFERENTIAL FORMS. MULTIPLE INTEGRALS. IMPLICIT FUNCTION THEOREM. DIVERGENCE THEOREM. STOKES FORMULA. PART II SEQUENCES OF FUNCTIONS. SERIES OF FUNCTIONS. POWER SERIES FUNCTIONS. TAYLOR SERIES. FOURIER SERIES. ORDINARY DIFFERENTIAL EQUATIONS: INTRODUCTION, ORDINARY EQUATIONS, EXISTENCE AND UNIQUENESS OF SOLUTIONS OF CAUCHY PROBLEMS, LINEAR EQUATIONS, SOLUTION METHODS. EXACT DIFFERENTIAL EQUATIONS. BOUNDARY VALUE PROBLEMS. SYSTEMS OF DIFFERENTIAL EQUATIONS. PARTIAL DIFFERENTIAL EQUATIONS.

PART I
DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES. LINE INTEGRALS. DIFFERENTIAL FORMS. MULTIPLE INTEGRALS. IMPLICIT FUNCTION THEOREM. DIVERGENCE THEOREM. STOKES FORMULA.
PART II
SEQUENCES OF FUNCTIONS. SERIES OF FUNCTIONS. POWER SERIES FUNCTIONS. TAYLOR SERIES. FOURIER SERIES. ORDINARY DIFFERENTIAL EQUATIONS: INTRODUCTION, ORDINARY EQUATIONS, EXISTENCE AND UNIQUENESS OF SOLUTIONS OF CAUCHY PROBLEMS, LINEAR EQUATIONS, SOLUTION METHODS. EXACT DIFFERENTIAL EQUATIONS. BOUNDARY VALUE PROBLEMS. SYSTEMS OF DIFFERENTIAL EQUATIONS. PARTIAL DIFFERENTIAL EQUATIONS.

	Teaching Methods
	LECTURES.

	Verification of learning
	PREPARATION OF A SHORT THESIS AND OF EXERCISES. WRITTEN AND ORAL EXAMINATION.

	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. A.BACIOTTI - F.RICCI, LEZIONI DI ANALISI MATEMATICA 2, EDITRICE LEVROTTO & BELLA. 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. LAURENCE C. EVANS, PARTIAL DIFFERENTIAL EQUATIONS, GRADUATE STUDIES IN MATHEMATICS, VOL.19, AMERICAN MATHEMATICAL SOCIETY.

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.
A.BACIOTTI - F.RICCI, LEZIONI DI ANALISI MATEMATICA 2, EDITRICE LEVROTTO & BELLA.
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.
LAURENCE C. EVANS, PARTIAL DIFFERENTIAL EQUATIONS, GRADUATE STUDIES IN MATHEMATICS, VOL.19, AMERICAN MATHEMATICAL SOCIETY.