# Matematica | MATHEMATICAL ANALYSIS III

## Matematica MATHEMATICAL ANALYSIS III

 0512300008 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2010 PRIMO SEMESTRE
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
 LUCA ESPOSITO T
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.

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