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

SUBJECT

Code
Subject
MMA0013 Supplement of Mathematical Analysis
Section
Semester
Hours: C+S+L
Category
Type
Mathematics - in Romanian
6
2+1+0
speciality
optional
Mathematics-Computer Science - in Romanian
6
2+1+0
speciality
optional
Teaching Staff in Charge
Prof. DUCA Dorel, Ph.D.,  dducamath.ubbcluj.ro
Assoc.Prof. FINTA Zoltan, Ph.D.,  fzoltanmath.ubbcluj.ro
Aims
Presentation of the main complementary notions and results in Mathematical Analysis.
Content
1. Real numbers. Complements.
2. Sequences: upper and lower limits.
3. Upper and lower limits of functions.
4. Upper and lower semicontinuity.
5. Derivatives. Dini’s numbers.
6. Lagrange’s theorem: the determination of the position of an intermediate point, contraction intervals.
7. Lagrange’s theorem: properties of intermediate points.
8. Cauchy’s theorem: properties of intermediate points.
9. Taylor’s theorem: properties of intermediate points.
10. Mean theorems of integrals: properties of intermediate points.
11. Henstock-Kurzweil’s integral: definition, examples, characterization.
12. Properties of the Henstock-Kurzweil integral.
13. The connection between Henstock-Kurzweil integral and the Riemann integral.
14. The characterization of the antiderivative functions with the help of strong Henstock-Kurzweil integrable function.
References
1. D.I. Duca, E. Duca: Exercitii si probleme de analiza matematica, Editura Casa Cartii de Stiinta, Cluj-Napoca, 2007 (vol. 1), 2009 (vol. 2)
2. S. Leader: The Kurzweil-Henstock integral and its differentials: a unified theory of integration on R and R^n, Marcel Dekker, Inc., Basel, 2001
3. M. Megan: Bazele Analizei matematice, vol. 1,2,3, Editura Eurobit, 1997, 1997, 1998
4. A. Precupanu: Analiza matematica (Functii reale), Editura Didactica si Pedagogica, Bucuresti, 1976
5. Gh. Siretchi: Calcul diferential si integral, vol. I si II, Editura Stiintifica si Enciclopedica, Bucuresti,1985
6. Gh. Siretchi Gh.: Functii cu proprietatea Darboux, Universitatea din Bucuresti, Bucuresti, 1986
7. V.A. Zorich: Mathematical Analysis, Springer, Berlin,
Assessment
Exam.The activity ends with a written final exam (50%). During the semester, the students will have to prepare two reports (25%). The students’ activity during the semester will be also considered (25%).
All university official rules with respect to students’ attendance of academic activities, as well as to cheating and plagiarism, are valid and enforced.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject