Universitatea "Babes-Bolyai" Cluj-Napoca
Facultatea de Matematica si Informatica
FISA DISCIPLINEI
| Tehnici de simulare numerica cu Matlab |
trul |
||||
| 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 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 |