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	
MMN0003	Numerical Calculus	

Semester	Hours: C+S+L	Category	Status	
6	2+0+2	speciality	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.	Numerical and Statistical Calculus	*		*	

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

III. Course objectives
Basic course in numerical analysis. Knowledge of main notions and procedures from numerical analysis. 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, spline interpolation. Least squares approximation.
3. Linear and positive operators.
4. Linear functional approximation: numerical differentiation and integration. Newton-Cotes, Gauss, Chebyshev quadrature formulas.
5. Numerical solution of linear systems. Direct methods: LUP decomposition, Cholesky and QR decomposition. Stationary iterative methods: Jacobi, Gauss-Seidel, SOR.
6. Nonlinear equations. Equations in R: successive approximation, Newton’s method, secant’s method. Nonlinear systems: Newton’s method.
7. Differential equations. Runge-Kutta methods.	

V. Bibliography
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.	T. Cătinaş, Interpolation of scattered data,  "Casa Carţii de Ştiinţă",  2007.
4.	Gh. Coman, Analiză numerică, Ed. Libris, Cluj-Napoca, 1995.
5.	Gh. Coman, T. Cătinaş, şi alţii, Interpolation operators,  "Casa Carţii de Ştiinţă", Cluj-Napoca, 2004.
6.	Gh. Coman, I. Chiorean, T. Cătinaş, Numerical Analysis. An Advanced Course,  Presa Universitară Clujeană, 2007.
7.	D.D. Stancu, Gh. Coman, O. Agratini, R. Trimbitas, Analiză Numerică şi Teoria Aproximării, vol. I, Presa Universitară Clujeană, 2001;
8.	D.D. Stancu, Gh. Coman, P. Blaga, Analiză Numerică şi Teoria Aproximării, vol. II, Presa Universitară Clujeană, 2002; 
9.	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.
•	Course 3 : Lagrange interpolation.
•	Lab 3: Problems with finite and divided differences.
•	Course 4 : Hermite interpolation.
•	Lab 4: Problems with Lagrange interpolation. Aitken’s algorithm. 
•	Course 5: Birkhoff interpolation.
•	Lab 5: Problems with Hermite interpolation.
•	Course 6: Least squares approximation.
•	Lab 6 : Problems with least squares approximation for discrete and continuous case.
•	Course 7: Linear and positive operators
•	 Lab 7: Problems with Bernstein operator.
•	Course 8: Numerical differentiation and integration. Newton-Cotes, Gauss, Chebyshev quadrature formulas.
•	 Lab 8: Problems with numerical integration.
•	Course 9: Numerical solution of linear systems. Direct methods.
•	Lab 9: Problems for solving linear system with direct methods.
•	Course 10: Numerical solution of linear systems. Iterative methods.
•	Lab 10:. Problems for solving linear system with iterative methods.
•	Course 11: . Nonlinear equations. Equations in R: successive approximation, Newton’s method, secant’s method. Nonlinear systems: Newton’s method.
•	Lab 11:. Problems with Newton’s and secant’s methods
•	Course 12: Differential equations. Runge-Kutta methods.
•	 Lab 12:.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. W. Gautschi, Numerical Analysis. An introduction, Birkhauser, Basel, 1997.  	

	Dean,							Chair head,
            Prof. Leon Timbulea, Ph.D.                                     Prof. Petru Blaga, Ph.D.

	Date,							Course responsible,
	18.09.2008						Lect. CATINAS Teodora Maria, Ph.D.