Mathematical modelling 
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Teaching Staff in Charge 
 

Aims 
to present and solve some basic mathematical modells from various areas of science 
Content 
I. Mathematical modelling process
1. Introduction: Important steps in the mathematical history 2. Relation between mathematics and its applications 3. Mathematical modelling process 4. Simple mathematical models: a) Transports problem; b) Fibonacci's problem; c) Bank interest; d) Marketing expenses optimation II. Discrete mathematical models 1. Linear difference equations with constant coeficients 2. Linear systems of difference equations with constant coeficients 3. Nonlinear difference equation systems. equilibrium points, stability 4. Discrete mathematical models. The logistic difference equation, discrete multispecies models III. Populations dynamics 1. Dynamics of an operator 2. Discrete dynamical systems 3. Stationary steady, stability 4. Autonomous systems 5. Mathematical models governed by differential equations a) Unlimited growth model b) Limited growth model c) Models with sacrifices d) Preypredator models e) Mathematical models governed by differential equations with deviating argument f) SIR Epidemical models g) Periodicity phenomens in populations dynamics III. Spline functions 1. Spline functions efficient instrument in construction of optimal aproximation methods 2. Cubic spline functions, definition, construction 3. Cubic spline functions of interpolation 4. Convergence properties 5. Extremal convergence properties of cubic spline functions 6. Applications of spline functions in numerical treatment of equations 7. Histospline functions IV. General diffusion models 1. Modern theory of diffusion 2. A general model diffusionconvectionreaction 3. Multispecies diffusion models 
References 
1. RUS, IOAN A.  IANCU, CRACIUN: Modelare matematica, Editura Transilvania, ClujNapoca, 2000
2. IANCU, CRACIUN: Modelare matematica. Teme speciale. Ed. Casa Cartii de Stiinta, ClujNapoca, 2002 3. MURRAY,J.D.: Mathematical biology, SpringerVerlag, Berlin,1989. 4. FOWLER, A.C.: Mathematical models in applied sciences, Cambridge University Press, 1989. 5. ARAMA, OLEG: Aplicatii ale matematicii in farmacie si medicina, Ed. Dacia, ClujNapoca, 1987. 6. NARENDRA, S.  GOEL, S.  MAITRA, S.C.  MONTROL, E.W.: On the Volterra and other nonlinear models of interacting populations, Reviews of Modern Physics, 43, 2(1971), 231276. 7. AGARWAL, R.P.: Difference Equations and Inequalities, Marcel Dekker, 2000. 8. ELAYDI, S.N.: An Introduction to Difference Equations, Springer Verlag, 1996 
Assessment 
During the semester one test with 20% from final degree and final exam with 80% from final degree. 