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	Category	Status	
3	2+1+0	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

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

MATLAB

-      Sparse Matrices in MATLAB
-      Numerical Linear Algebra in MATLAB: systems, least squares, eigenvalues and eigenvectors, SVD
-      MATLAB Graphics; 3D, Volume Visualization, Animation
-      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
Lectures
Week 1 – Basic linear algebra
Week 2 – SVD and applications
Week 3 – Orthogonality and least squares
Week 4 – Error theory and conditioning of a problem
Week 5 – Linear systems, direct methods
Week 6 – Eigenvalues and eigenvectors
Week 7 - Eigenvalues and eigenvectors, nonsymmetric problems
Week 8 - Eigenvalues and eigenvectors, symmetric problems
Week 9 - Stationary Iterative Methods for  Linear Algebraic Systems: Jacobi, Gauss-Seidel, SOR
Week 10 - Nonstationary Iterative Methods for  Linear Algebraic Systems: conjugate gradient, GMRES, BICG
Week 11 - Iterative Methods for Eigenvalues and Eigenvectors: Arnoldi, Lanczos
Week 12 - Sparse Matrices - representation, operations, algorithms, black boxes
Labs
Week 2 -- 3d Matlab graphics and animation
Week 4 – SVD
Week 6 – ODEs in MATLAB
Week 8 – Error and condition
Week 10 - Eigenvalues
Week 12 – Nonstationary iterative methods	

VII. Didactic methods used
Computer presentation, experiment
Expositions: description, explanation, class lectures, dialog-based lectures, lectures with demonstrations, introductive lectures, current lectures, synthesis lectures. 
Conversations: debate, dialog, introductive conversations, conversations for knowledge consolidation, conversations to systematize and synthesize knowledge 
Use of problems: use of problem questions, problems and problem situations. 
Discovery: directed and independent rediscovery, creative discovery, inductive discovery, deductive discovery, discovery by documenting, experimental discovery. 
Other methods: case study; cooperation, simulation, brainstorming, individual study, exercise, homework study.

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

IX. Additional references
4. R. Trîmbiţaş – Numerical Analysis in MATLAB, Presa Universitară Clujeana, 2009	

	Dean,							Chair head,

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