# Fisica | MATHEMATICAL ANALYSIS II

## Fisica MATHEMATICAL ANALYSIS II

 0512600002 DIPARTIMENTO DI FISICA "E.R. CAIANIELLO" PHYSICS 2013/2014

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2010 ANNUALE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 8 64 LESSONS BASIC COMPULSORY SUBJECTS MAT/05 4 48 LAB 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.
THE GOAL OF THE COURSE IS TO INDUCE THE STUDENTS TO DESCRIBE CLEARLY AND IN A COMPLETE WAY THE SUBJECTS STUDIED. ABILITY OF INDEPENDENT OPINIONS IS REQUIRED.

Prerequisites
GOOD KNOWLEDGE OF THE SUBJECTS CONTAINED IN THE COURSE ANALISI MATEMATICA I.
Contents
DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES. 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. BASIC KNOWLEDGE IN FUNDAMENTAL PROPERTIES OF MULTIPLE INTEGRALS, DIVERGENCE THEOREM, GAUSS-GREEN FORMULA. KNOWLEDGE OF BASIC PROPERTIES OD DIFFERENTIAL FORMS, STOKES FORMULA. ABILITY TO SOLVE OPTIMIZATION PROBLEMS USING LAGRANGE MULTIPLIERS.
Teaching Methods
LECTURES.
Verification of learning
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.
S.SALSA - A.SQUELLATI, ESERCIZI DI ANALISI MATEMATICA 2, PARTE PRIMA, SERIE NUMERICHE E SERIE DI FUNZIONI, ZANICHELLI ED.
S.SALSA - A.SQUELLATI, ESERCIZI DI ANALISI MATEMATICA 2, PARTE TERZA, EQUAZIONI DIFFERENZIALI ORDINARIE, ZANICHELLI ED.
LAURENCE C. EVANS, PARTIAL DIFFERENTIAL EQUATIONS, GRADUATE STUDIES IN MATHEMATICS, VOL.19, AMERICAN MATHEMATICAL SOCIETY.