Disciplina: Tehnici de simulare numerica cu Matlab	Cod: ME046	

Semestrul	Ore: C+S+L	Tipul	Specializarea	
8	2+0+2	optionala	Informatica	
8	2+0+2	obligatorie	Matematici aplicate	

Cadre didactice indrumatoare	Prof. Dr. TRIF Damian, dtrif@math.ubbcluj.ro	
Obiective	Studentii vor invata cum sa-si imbine cunostintele matematice de baza cu metodele numerice si tehnicile de programare pentru a rezolva problemele puse de practic	
Continut	1. Probleme practice care conduc la ecuatii diferentiale si cu derivate partiale. Modelare matematica. Probleme inverse. 
 2. Aproximarea functiilor, aritmetica intervalelor (pachetul INTLAB), vizualizarea, influenta erorilor de rotunjire, rezultate paradoxale ale calculului, derivare automata.
 3. Studii calitative ale modelelor; puncte singulare, bifurcatii, etc.
 4. Regularizarea problemelor rau conditionate 
 5. Shadowing si validarea rezultatelor simularii
 6. Chebfun, LiScM, accdot	
Bibliografie selectiva	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.	
Evaluare	proiect 50%, examen final 50