Subject: Numerical Simulation Techniques Using MATLAB	Code: ME046	

Semester	 Hours: C+S+L	Type	 Section	
8	2+0+2	optional	Computer Science	
8	2+0+2	compulsory	Applied Mathematics	

Teaching Staff in Charge	Prof. TRIF Damian, Ph.D., dtrif@math.ubbcluj.ro	
Aims	The course is aimed at those who are active in computer simulation or are planning to become so. In effect, the student will learn to couple his/her understanding of basic mathematics with numerical methods in order to obtain solutions to engineering problems	
Content	1. Practical problems, models,inverse problems
2. Automatic differentiation and interval arithmetic (INTLAB package)
3. Qualitative studies, singular points, bifurcations
4. Ill-conditionned problems, regularization
5. Shadowing and validation of numerical results
6. Chebfun, LiScM, accdo	
Selective References	Hairer E., Numerical Geometric Integration, Internet course, 1999, http://www.unige.ch/math/folks/hairer/polycop.html
Hargreaves G. I., Interval Analysis in MATLAB, Numerical Analysis Report No. 416, Univ. of Manchester, 2002, http://www.ma.man.ac.uk/~nareports
Lynch S., Dynamical Systems with Applications using MATLAB, Birkhäuser, 2004.
Morosanu Gh., Ecuatii diferentiale. Aplicatii, Ed. Academiei RSR, 1989.
Parker T. S., Chua L. O., Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, 1989.
Stauning O., Automatic Validation of Numerical Solutions, IMM-PHD-1997-36, Thesis, Lyngby, 1997, http://citeseer.nj.nec.com/stauning97automatic.html
Trif D., Metode numerice in teoria sistemelor dinamice, Transilvania Press, 1997.
Watson H. A. Jr., Differential Equations for Reliability, Maintainability, and Availability, Internet course, 1997, http://mathforum.org/differential/watson/
Zeldovich Ya. B., Myąkis A. D., Elements of Applied Mathematics, Mir Publishers Moskow, 1976.	
Assessment	individual project 50%, final exam 50