# Matematica | MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II

## Matematica MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II

 0512300001 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2013/2014

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2010 ANNUALE
 SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY 1 ANALISI MATEMATICA I MAT/05 6 48 LESSONS BASIC COMPULSORY SUBJECTS MAT/05 3 36 EXERCISES BASIC COMPULSORY SUBJECTS 2 ANALISI MATEMATICA II MAT/05 5 40 LESSONS BASIC COMPULSORY SUBJECTS MAT/05 3 36 EXERCISES BASIC COMPULSORY SUBJECTS
 MARIA TRANSIRICO21 T SARA MONSURRO'1
Objectives
THE COURSE OF "ANALISI MATEMATICA I/ANALISI MATEMATICA II" IS ESSENTIALLY DEVOTED TO THE STUDY OF REAL FUNCTIONS OF A REAL VARIABLE, TO THE THEORY OF LIMITS AND TO THE DIFFERENTIAL AND INTEGRAL CALCULUS FOR SUCH FUNCTIONS, AND TO THE STUDY OF NUMERICAL SERIES. THE AIM OF THE COURSE IS THE ACQUISITION OF RESULTS, PROOFS AND CALCULATION TECHNIQUES.
Prerequisites
BASIC KNOWLEDGE ACQUIRED THROUGH HIGH SCHOOL COURSES. IN PARTICULAR, KNOWLEDGE OF ELEMENTARY ALGEBRA, TRIGONOMETRY AND FIRST AND SECOND ORDER INEQUALITIES IS REQUIRED.
Contents
1. ALGEBRAIC STRUCTURES: DEFINITIONS AND EXAMPLES.
2. REAL NUMBERS.
3. REAL FUNCTIONS.
4. COMPLEX NUMBERS.
5. LIMITS OF SEQUENCES.
6. LIMITS OF FUNCTIONS AND CONTINUOUS FUNCTIONS.
7. MORE ON LIMITS.
8. DERIVATIVES.
9. APPLICATION OF DIFFERENTIAL CALCULUS. GRAPHS OF FUNCTIONS.
10. RIEMANN INTEGRATION.
11. INTEGRAL CALCULUS
12. TAYLOR'S FORMULA.
13. NUMERICAL SERIES.
Teaching Methods
•FRONTAL LESSON•PRACTICE LESSON
Verification of learning
WRITTEN TEST AND ORAL EXAMINATION.
Texts
P. MARCELLINI - C. SBORDONE, ANALISI MATEMATICA UNO, LIGUORI EDITORE.
P. MARCELLINI - C. SBORDONE, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE.
A. ALVINO - L. CARBONE - G. TROMBETTI, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE.
M. TROISI, ANALISI MATEMATICA I, LIGUORI EDITORE.
D. GRECO - G. STAMPACCHIA, ESERCITAZIONI DI MATEMATICA, VOL. I, LIGUORI EDITORE.