Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MM275	Computational Mechanics	

Section	Semester	Hours: C+S+L	Category	Type	
Computational Mathematics - in Hungarian	1	2+2+0		compulsory	

Teaching Staff in Charge	Assoc.Prof. SZENKOVITS Ferenc, Ph.D., fszenko@math.ubbcluj.ro	
Aims	The aim of this course is to give a short introduction in modeling of dynamical systems with a finite number of degrees. Students absolving this course will be able to study dynamical problems using Lagrangian end Hamiltonian formalism. They will be able to study various phenomenon using numerical methods.	
Content	I. Mathematical methods for differential equations
   1. Models and differential equations
   2. Models and mathematical problems
   3. Stability and perturbation methods
II. Mathematical methods of classical mechanics
   1. Dynamical systems and Newtonian dynamics
   2. Lagrangian dynamics
   3. Hamiltonian dynamics and Hamilton-Jacobi Theory
III. Chaotic dynamics, stability and bifurcations
   1. Stability diagrams
   2. Limit cycles
   3. Hopf bifurcation
   4. Chaotic motions
IV. Numerical methods for ordinary differential equations
   1. Numerical methods for initial-value problems
   2. Numerical methods for boundary-value problems
V. Applications
	
Bibliography	1. ARNOLD, V.I.: Metodele matematice ale mecanicii clasice, Editura Stiintifica si Enciclopedica, Bucuresti, 1980.
2. BELLAMO, N., PREZIOSI, L., ROMANO, A.: Mechanics and Dynamical Systems with Mathematica, Birkhauser, 2000. 
3. BUTCHER, J. C.: The numerical analysis of ordinary differential equations. John Wiley  Sons, 1987.
4. DRAGOS, L.: Principiile mecanicii analitice, Editura Tehnica, Bucuresti, 1976.
5. BÁLINT, ÉRDI: The dynamics of the Solar System, ELTE Eötvöos Kiadó, Budapest, 2001  (Hungarian).
6. NAKAMURA, S.: Numerical analysis and graphic visualization with Matlab, Prestice Hall PTR, New-Jersey, 1996.
7. PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T., FLANNERY, B. P.: Numerical Recipes in C, The Art of Scientific Computing, Second Edition, Cambridge University Press, Cambridge, New York, Port-Chester, Melbourne, Sydney, 1992.
8. SZENKOVITS F., MAKO Z., CSILLIK I., BÁLINT, A.: Mechanikai rendszerek számítógépes modellezése, Ed. Sapientia, Cluj-Napoca, 2002.
	
Assessment	Project - 50% and a practical verification - 50%.