# 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

 LOREDANA CASO21
ExamDate
ANALISI M,ATEMATICA I / ANALISI MATEMATI14/04/2023 - 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
12. TAYLOR'S FORMULA.
13. NUMERICAL SERIES.
Teaching Methods
•FRONTAL LESSON 9 CFU
•PRACTICE LESSON 7 CFU
Verification of learning
THE EXAMINATION TEST IS FINALIZED TO ASSESS THE KNOWLEDGE AND CONFIDENTIAL CAPACITY OF THE CONCEPTS SUBMITTED IN LESSON AND THE CAPACITY TO APPLY THESE KNOWLEDGE.
THE EXAMINATION TEST IS PROVIDED IN A WRITTEN TEST FOLLOWING AN ORAL TEST. TO BE SUBMITTED TO SUPPORT THE ORAL TEST, THE STUDENT MUST HAVE SUFFICIENT EVALUATION IN THE WRITTEN TEST. WRITING TEST IS 'EXERCISING TYPE', WHILE THE ORAL TEST IS 'THEORETICAL TYPE'. THE EXAMINATION MAY BE REPLACED BY TWO INTERMEDIATE TESTS OF THE SAME TYPE.
IN THE FINAL EVALUATION, THE WRITTEN TEST ASSESSMENT SHALL BE 40% WHEN THE ORAL TEST FOR THE 60% RESELLER. THE LODES MAY BE ATTRIBUTED TO STUDENTS DESIGNING TO BE ATTENDED TO APPLY AUTONOMY KNOWLEDGE AND COMPETENCES ACQUISITE EVEN IN OTHER DISPUTES FROM THESE PROPOSED LESSONS.
Texts
C.PAGANI- S.SALSA, ANALISI MATEMATICA 1, ZANICHELLI.
M. TROISI, ANALISI MATEMATICA I, LIGUORI EDITORE.
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.
D. GRECO - G. STAMPACCHIA, ESERCITAZIONI DI MATEMATICA, VOL. I, LIGUORI EDITORE.