Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MO009	Advanced Mathematical Analysis	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	7	2+2+0		optional	
Mathematics-Computer Science - in Hungarian	7	2+2+0		optional	

Teaching Staff in Charge	Lect. FINTA Zoltan, Ph.D., fzoltan@math.ubbcluj.ro	
Aims	Presentation of the main complementary notions and results in Mathematical Analysis.	
Content	1.Inequalities.
 2. Sequences. Generalizations of the notion of limit.
 3. Limits of functions. Generalizations of the notion of limit of a function.
 4. Continuous functions. Generalizations of the notion of continuity. Special classes of continuous functions.
 5. Generalization of the notion of derivativ. Generalizations of the mean theorems of the differential calculus. 
 6. Integrable functions. Generalization of the notion of the integral. The role of the systems of intermediary points in the definition of the integral.	
Bibliography	1. Siretchi Gh.: Functii cu proprietatea Darboux, Universitatea din Bucuresti, 
   Bucuresti, 1986.
2. Leader S.: The Kurzweil-Henstock integral and its differentials: a unified theory of   
   integration on R and R^n, Marcel Dekker, Inc., Basel, 2001.
3. Precupanu A.: Analiza matematica (Functii reale), Editura Didactica si Pedagogica,
   Bucuresti, 1976.
4. Balazs M. - Kolumban J.: Matematikai Analizis, Dacia Konyvkiado, Koloszvar, 1978.
5. Szokefalvi-Nagy B.: Valos fuggvenyek es fuggvenysorok, Tankonyvkiado, Budapest, 1977.

Assessment	Exam.