Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Calculatoare şi tehnologia informaţiei
Programul de studii: Ingineria informatiei - in limba engleza
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMP0008	Numerical Methods	

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

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
CATINAS Teodora Maria	Ph.D.	Lect.	Applied Mathematics	*			

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

III. Course objectives
Being a basic course in numerical analysis, the objectives are: knowledge of main notions and procedures from numerical analysis and the ability to work with them. The course is oriented to numerical algorithms and implementation of numerical software.	

IV. Course contents
1. Error theory and floating-point arithmetic. Linear spaces. Orthogonal polynomials. Finite and divided differences.
2. Interpolation of functions: Lagrange, Hermite, Birkhoff. 
3. Linear functional approximation: numerical differentiation and integration. Newton-Cotes formulas. Repeated quadrature formulas. 
4. Gauss and Chebyshev quadrature formulas. Adaptive quadratures.
6. Numerical methods for solving linear systems: direct methods (Gauss) and iterative methods (Jacobi, Gauss-Seidel, SOR).
7. Numerical methods for solving nonlinear equations: successive approximation, Newton’s method, secant’s method; and nonlinear systems: Newton’s method.
8. Numerical methods for solving differential equations.
9. Linear and positive operators.	

V. Bibliography
1.	1. O. Agratini, P. Blaga, Gh. Coman, Lectures on Wavelets, Numerical Methods, and Statistics, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005. 
2.	O. Agratini, I. Chiorean, Gh. Coman, R.T. Trîmbitaş, Analiză Numerică şi Teoria Aproximării, vol. III, Presa Universitară Clujeană, 2002; 
3.	I. Chiorean, Analiza numerica, Ed. Presa Univ. Clujeana, 2010.
4.	Gh. Coman, T. Cătinaş, şi alţii, Interpolation operators,  "Casa Carţii de Ştiinţă", Cluj-Napoca, 2004.
5.	Gh. Coman, I. Chiorean, T. Cătinaş, Numerical Analysis. An Advanced Course,  Presa Universitară Clujeană, 2007.
6.	D.D. Stancu, Gh. Coman, O. Agratini, R. Trimbitas, Analiză Numerică şi Teoria Aproximării, vol. I, Presa Universitară Clujeană, 2001;
7.	D.D. Stancu, Gh. Coman, P. Blaga, Analiză Numerică şi Teoria Aproximării, vol. II, Presa Universitară Clujeană, 2002; 
8.	R. Trîmbitaş, Numerical Analysis, Presa Universitară Clujeană, 2007.

VI. Thematic of didactic activities per weeks
•	Course 1 : Error theory and floating-point arithmetic. Linear spaces. Orthogonal polynomials. 
•	Lab 1: Introductory problems and examples in Matlab. 
•	Course 2 : Finite and divided differences.
•	Lab 2: Problems for error theory and orthogonal polynomials. Computation of finite and divided differences.
•	Course 3 : Lagrange interpolation.
•	Lab 3: Computation of Lagrange polynomial using baricentric formula.
•	Course 4 : Hermite interpolation.
•	Lab 4: Applied problems to Lagrange interpolation using Aitken’s algorithm. 
•	Course 5: Birkhoff interpolation.
•	Lab 5: Applied problems to Hermite interpolation.
•	Course 6: Numerical differentiation and integration. Newton-Cotes quadrature formulas. Repeated quadrature formulas
•	 Lab 6: Problems with numerical integration formulas.
•	Course 7:  Gauss and Chebyshev quadrature formulas. Adaptive quadratures.
•	Lab 7: Problems applied to adaptive quadratures.
•	Course 8: Numerical methods for solving linear systems - direct methods.
•	Lab 8: Problems for solving linear systems with direct methods.
•	Course 9: Numerical methods for solving linear systems - iterative methods.
•	Lab 9:. Problems for solving linear systems with iterative methods.
•	Course 10: . Methods for solving nonlinear equations in R: successive approximation method, Newton’s method, secant’s method. 
•	Lab 10:. Problems with Newton’s and secant’s methods for solving nonlinear equations.
•	Course 11: Methods for solving nonlinear systems: successive approximation method and Newton’s method.
•	Lab 11:. Problems with Newton’s method for solving nonlinear systems.
•	 Course 12: Numerical methods for solving differential equations.
•	 Lab 12: Solving some differential equations. Ending of evaluation for laboratories.
•	Course 13: Linear and positive operators.
•	 Lab 13: Problems with Bernstein operator.
•	Course 14: Summary of the main results.
•	 Lab 14: Ending of evaluation for laboratories.	

VII. Didactic methods used
Lectures, interactive presentations, exercises, homework assignments.	

VIII. Assessment
The score is computed as (70%score of final test+30%score for laboratory).	

IX. Additional references
1.	T. Cătinaş, Interpolation of scattered data,  "Casa Carţii de Ştiinţă",  2007.
2.	Gh. Coman, Analiză numerică, Ed. Libris, Cluj-Napoca, 1995.	

Dean,							Chair head,
Prof. Leon Timbulea, Ph.D.                                     Prof. Octavian Agratini, Ph.D.

	Date,							Course responsible,
            27.10.2010						Lect. CATINAS Teodora Maria, Ph.D.