Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare si simulare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMC1009	Numerical Methods in Simulation	

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

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
TRÎMBITAS Radu Tiberiu	Ph.D.	Assoc.Prof.	Applied Mathematics	*			

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

III. Course objectives
To learn student to apply Numerical Analysis techniques to Simulation

IV. Course contents
Numerical Linear Algebra

&#183;       Matrix Analysis - matrix norms, sequences of matrices
&#183;       Singular Value Decomposition (SVD), properties, applications
&#183;       Orthogonality, QR Decomposition, Householder reflections, Givens rotations,    applications to Least Squares Problems, SVD and least squares
&#183;       Condition of a problem and of an algorithm, Floating Point Arithmetic, machine epsilon, cancelation, IEEE standard, Stability and Backward Stability
&#183;       Direct Methods for Linear Algebraic Systems: GEPP, Cholesky
&#183;       Eigenvalues and Eigenvectors, properties, power method, inverse iteration, QR. Symmetric eigenvalue problems.
&#183;       Stationary Iterative Methods for  Linear Algebraic Systems: Jacobi, Gauss-Seidel, SOR
&#183;       Nonstationary Iterative Methods for  Linear Algebraic Systems: conjugate gradient, GMRES, BICG
&#183;       Iterative Methods for Eigenvalues and Eigenvectors: Arnoldi, Lanczos
&#183;       Sparse Matrices - representation, operations, algorithms, black boxes

MATLAB

&#183;       Sparse Matrices in MATLAB
&#183;       Numerical Linear Algebra in MATLAB: systems, least squares, eigenvalues and eigenvectors, SVD
&#183;       MATLAB Graphics &#8211; 3D, Volume Visualization, Animation
&#183;       ODE Solvers - one-step, multistep, stiffness, event-handling

V. Bibliography
1. Demmel, James - Applied Numerical Linear Algebra, SIAM, 1997
2. Agratini, Octavian, Chiorean, Ioana, Coman, Gheorghe, Trimbitas, Radu,- Analiza numerica si Teoria aproximarii, vol. III, Presa Universitara Clujeana, 2002
3. Trefethen, Lloyd N., Bau III, David, - Numerical Linear Algebra, SIAM, 1997

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Exam 40%, Practical exam 40%, semester activity 20%	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. TRÎMBITAS Radu Tiberiu, Ph.D.