Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MME1011 | Differential Equations with Applications |
| Teaching Staff in Charge |
Lect. ANDRAS Szilard Karoly, andrasz math.ubbcluj.ro |
| Aims |
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An interdisciplinary introduction to modeling (economical, biological, chemical models) with dynamical systems. The study of stability and chaotic behavior, simulations.
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| Content |
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1. Introduction and historical aspects
2. Mathematics and its applications 3. The process of mathematical modelling 4. Discrete and continuous dynamical systems 5. Models for population biology 6. Steady states, stability 7. Autonomous systems, the study of stability 8. Epidemiologic models 9. The Lorenz model and chaotic behavior 10. Traffic simulation on a highway |
| References |
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1. RUS, IOAN A. - IANCU, CRACIUN: Modelare matematica, Editura Transilvania, Cluj-Napoca, 2000
2. IANCU, CRACIUN: Modelare matematica. Teme speciale. Ed. Casa Cartii de Stiinta, Cluj-Napoca, 2002 3. MURRAY,J.D.: Mathematical biology, Springer-Verlag, Berlin,1989. vol I+II 4. ARROWSMITH, Dynamical systems, Differential equations, maps and chaotic behaviour, Chapmann and Hall, 1992 5. ANDRÁS SZILÁRD: Dinamikus rendszerek, Editura didactica si pedagogica, 2008 6. LOUIS G. BIRTA, GILBERT ARBEZ: Modelling and Simulation, Springer, 2007 7. MIKLÓS FARKAS: Dynamical models in biology, Academic Press, 2001 8. D.R. SCHIER, K.T. WALLENIUS: Applied multidisciplinary modeling, Chapman and Hall, 1999 9. D.R. SCHIER, K.T. WALLENIUS: Applied multidisciplinary modeling, 10. NINO BOCCARA: Modelling complex systems, Springer, 2004 |
| Assessment |
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Activity (courses and seminars): 30%
Project: 40% Final exam 30% If a student’s absentees is greater than 40% from the number of all activities, the student has to prepare a special presentation (paper) in a subject specified by the professor. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |