Fisica | CALCULUS II

Fisica CALCULUS II

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

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2016 ANNUALE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 12 96 LESSONS BASIC COMPULSORY SUBJECTS
 ANNA CANALE T LUCA ESPOSITO
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.
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.