# Matematica | MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II

## Matematica MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II

 0512300001 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2018 FULL ACADEMIC YEAR
 SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY 1 ANALISI MATEMATICA I MAT/05 8 64 LESSONS BASIC COMPULSORY SUBJECTS 2 ANALISI MATEMATICA II MAT/05 8 64 LESSONS BASIC COMPULSORY SUBJECTS

 SARA MONSURRO'21
ExamDate
ANALISI MATEMATICA I / ANALISI MATEMATIC19/04/2023 - 14:00
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.
11. INTEGRALI INDEFINITI.
12. IMPROPER INTGERALS.
13. TAYLOR'S FORMULA.
14. NUMERICAL SERIES.
Teaching Methods
THEORY 9 CFU • EXERCISES 7 CFU
Verification of learning
THE EXAMINATION TEST IS FINALIZED TO ASSESS THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS STUDIED DURING THE COURSE AND THE CAPACITY TO APPLY THESE KNOWLEDGE.
THE EXAMINATION TEST CONSISTS IN A WRITTEN TEST FOLLOWED BY AN ORAL TEST. TO ACCESS TO THE ORAL TEST, THE STUDENT MUST HAVE A SUFFICIENT EVALUATION IN THE WRITTEN PART. THE WRITTEN TEST MAY BE REPLACED BY TWO INTERMEDIATE TESTS OF THE SAME TYPE.
Texts
P. MARCELLINI - C. SBORDONE, ANALISI MATEMATICA UNO, LIGUORI EDITORE.
C.PAGANI- S.SALSA, ANALISI MATEMATICA 1, ZANICHELLI.
M. TROISI, ANALISI MATEMATICA I, LIGUORI EDITORE.
P. MARCELLINI - C. SBORDONE, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE.
A. ALVINO - L. CARBONE - G. TROMBETTI, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE.
D. GRECO - G. STAMPACCHIA, ESERCITAZIONI DI MATEMATICA, VOL. I, LIGUORI EDITORE.