Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMA0002	Mathematical Analysis	

Semester	Hours: C+S+L	Category	Status	
1	3+2+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
MURESAN Marian	Ph.D.	Prof.	Mathematical Analysis and Optimization	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Getting to know the topology of IRn and the basic notions and results concerning the multivariable differential calculus.	

IV. Course contents
1. Real numbers. Sequences and series of real numbers.
2. Topology of IRn space.
3. Limites of real and vectorial functions of one and several variables.
4. Continuity and uniform continuity of real and vectorial functions of one and several variables
5. Differential calculus on R. The derivative and the differential of a real function. Operations with differentiable functions. Differentiability of the compound function and of the inverse function. Mean value theorems (Fermat, Rolle, Cauchy, Lagrange). L'Hospital rule. Higher order derivatives. The characterization of convexity by the sign of derivatives. Taylor formula. Local extrem points of a real function and their characterization.
6. Partial derivatives and differentiability of real and vector functions of several variables; Taylor's formula for real function of several variables. 
7. The inverse function theorem; differentiable implicit functions.
8. Optimality conditions; optimization problems having equations as constraints.

The basic notions and results concerning the multivariable differential and integral calculus are presented. The main topics included are: differentiability of vector functions of vector variable, mean value theorems for differentiable functions, partial derivatives, optimality conditions, the inverse function theorem, differentiable implicit functions, optimization problems having equations as constraints

V. Bibliography
1. ANDRICA D., DUCA I.D., PURDEA I., POP I.: Matematica de baza. Cluj-Napoca, Editura Studium, 2002.
2. BALAZS M., KOLUMBAN I.: Analiza matematica. Curs litografiat, Facultatea de Matematica, Univ. "Babes-Bolyai".
3. BRECKNER W. W.: Analiza matematica. Topologia spatiului Rn. Cluj-Napoca, Universitatea, 1985.
4. COBZAS ST.: Analiza matematica (Calcul diferential). Cluj-Napoca, Presa Universitara Clujeana, 1998. 
5. LUPSA L., BLAGA R.L. Elemente de analiza matematica si teoria campului. Partea I. Bistrita, Editura George Cosbuc, 2001. 
6. LUPSA L., BLAGA R.L. Elemente de analiza matematica si teoria campului. Partea I. Cluj-Napoca, Ed. RISOPRINT, 2002.
7. MARUSCIAC I.: Analiza matematica. I, II. Cluj-Napoca, Universitatea "Babes-Bolyai", 1980.
8. FIHTENHOLT G. M.: Curs de calcul diferential si integral. Vol. I, II. Bucuresti, Editura Tehnica, 1965.
9. TRIF T.: Probleme de calcul diferential si integral in IRn. Cluj-Napoca Ed. Casa Cartii de stiinta, 2003.
10. MEGAN M. Basele analizei matematice. Timisoara Ed. BIT, vol I - III, 2000, 2001, 2002.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Exam.	

IX. Additional references

	Date,							Course responsible,
								Prof. MURESAN Marian, Ph.D.