Universitatea "Babes-Bolyai" Cluj-Napoca
Facultatea de Matematica si Informatica
FISA DISCIPLINEI

Tehnici de simulare numerica cu Matlab
Cod
Semes-
trul
Ore: C+S+L
Tipul
Specializarea
ME046
8
2+0+2
optionala
Informatica
ME046
8
2+0+2
obligatorie
Matematici aplicate
Cadre didactice indrumatoare
Prof. Dr. TRIF Damian,  dtrifmath.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 practica
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
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., Myškis A. D., Elements of Applied Mathematics, Mir Publishers Moskow, 1976.
Evaluare
proiect 50%, examen final 50%
Legaturi: Syllabus-urile tuturor disciplinelor
Versiunea in limba engleza a acestei discipline
Versiunea in format rtf a acestei discipline