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

Code	Subject	
MMC1002	Special Topics in Numerical Analysis	

Section	Sem.	Hours: C+S+L	Category	Type	
Applied Mathematics	2	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Lect. CATINAS Teodora Maria, Ph.D., tcatinas@math.ubbcluj.ro	
Aims	The study of some modern procedures of approximation and interpolation, numerical integration, and of solving some differential equations.	
Content	1. Introductive notions.
2. Polynomial spline interpolation operators.
3. Interpolation operators on a rectangular domain. Examples of interpolation operators on a square and a cube.
4. Interpolation operators on a simplex domain. Examples of interpolation operators on a triangle and a tetrahedron. Newton@s Algorithm.
5. Interpolation operators on a triangle and a tetrahedron with curved sides.
6. Interpolation operators on an arbitrary domain. Extension of some calssical interpolation procedures. Univariate and bivariate Shepard interpolation. Interpolation by radial basis functions. 
7. Numerical integration of functions. Classical quadrature formulas. Richardson@s formula. Adaptive quadrature formulas. 
8. Optimal quadrature formulas in sense of Sard and Nikolski. Homogenous cubature  formulas.
9. Numerical methods for solving some differential equations.	
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

Assessment	The score is computed as: 70% score of final test + 30% score for activity during the semester.