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.	Applied Mathematics	*			

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. Adaptive quadrature formulas.
5. Direct methods for solving linear systems: LUP decomposition, Cholesky and QR decomposition, Gauss method.
6. Stationary iterative methods for solving linear systems: Jacobi, Gauss-Seidel.
7. Nonlinear equations. Equations in R: successive approximation, Newton’s method, secant’s method. Nonlinear systems: Newton’s method.
8. Differential equations. Runge-Kutta methods.	

V. Bibliography
1.	O. Agratini, I. Chiorean, Gh. Coman, R.T. Trîmbitaş, Analiză Numerică şi Teoria Aproximării, vol. III, Presa Universitară Clujeană, 2002; 
2.	T. Cătinaş, Interpolation of scattered data,  "Casa Carţii de Ştiinţă",  2007.
3.	Gh. Coman, Analiză numerică, Ed. Libris, Cluj-Napoca, 1995.
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.
•	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: Adaptive quadrature formulas. Romberg’s algorithm.
•	Lab 9: Problems with adaptive quadrature formulas and Romberg’s algorithm.
•	Course 10: Numerical solution of linear systems. Direct methods.
•	Lab 10: Problems for solving linear systems with direct methods.
•	Course 11: Numerical solution of linear systems. Iterative methods.
•	Lab 11:. Problems for solving linear systems with iterative methods.
•	Course 12: . Nonlinear equations in R: successive approximation, Newton’s method, secant’s method. 
•	Lab 12:. Problems with Newton’s and secant’s methods. 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. dr. Leon Tambulea                                         Prof. dr. Octavian Agratini

	Date,							Course responsible,
	25.11.2009						Lect. CATINAS Teodora Maria, Ph.D.