Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises.
Saturday, April 14, 2007
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Lesson 17, Wednesday, May 23, 2007 (+37 h)
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises.
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises.
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Lesson 19 , Thursday, May 24, 2007 (+41 h)
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises. 
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises.
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Lesson 16, Tuesday, May 22, 2007 (+34 h)
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises. 
Models of PDEs, terms of transport, the budget principles, reaction-diffusion theory, various examples and exercises.
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Lesson 15, Thursday, May 17, 2007 (+32 h)
series of exercises on discrete systems (equilibrium, stability, existence of periodic orbits 2.3, etc) in preparation for the final exam of the course. 
series of exercises on discrete systems (equilibrium, stability, existence of periodic orbits 2.3, etc) in preparation for the final exam of the course.
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Lesson 14, Wednesday May 16, 2007 (+30 h)
lesson on DNA, history of discovery, models and equations of bond. 
lesson on DNA, history of discovery, models and equations of bond.
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Lesson 13, Tuesday, May 15, 2007 (+27 h)
lesson devoted to the study of Lotka-Volterra type models presenting the phenomenon of large swings starting from certain points in the neighborhood of a configuration of stable equilibrium. Also it is a simple model like Lotka-Volterra type of cooperatives, to show how, in this case, each species benefits by the presence of increasing its maximum level sustainable by the environment. 
lesson devoted to the study of Lotka-Volterra type models presenting the phenomenon of large swings starting from certain points in the neighborhood of a configuration of stable equilibrium. Also it is a simple model like Lotka-Volterra type of cooperatives, to show how, in this case, each species benefits by the presence of increasing its maximum level sustainable by the environment.
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Lesson 12, Thursday, May 10, 2007 (+25 h)
lesson dedicated to the system of Lorentz (Lorentz attractor). 
lesson dedicated to the system of Lorentz (Lorentz attractor).
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Lesson 11, Wednesday, May 9, 2007 (+23 h)
Linear model of interaction between populations (Law of Malthus for each of the two populations linearly coupled with each other). Model of Lotka-Volterra (predator-prey) in the presence of unlimited resources for prey. Lotka-Volterra model with limited resources. For each model, determination and study of stability of equilibrium. Principle of competitive exclusion (the extinction of species less adapted). 
Linear model of interaction between populations (Law of Malthus for each of the two populations linearly coupled with each other). Model of Lotka-Volterra (predator-prey) in the presence of unlimited resources for prey. Lotka-Volterra model with limited resources. For each model, determination and study of stability of equilibrium. Principle of competitive exclusion (the extinction of species less adapted).
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Lesson 10, Tuesday, May 8 2007 (+20 h)
the Fibonacci sequence. Golden section. Studio finite difference equations in several steps. Resolution with explicit solutions of the characteristic equation. Special solutions of the equation is not homogeneous. Equilibrium and stability conditions of equilibria. 
the Fibonacci sequence. Golden section. Studio finite difference equations in several steps. Resolution with explicit solutions of the characteristic equation. Special solutions of the equation is not homogeneous. Equilibrium and stability conditions of equilibria.
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Lesson 9 Wednesday, May 2, 2007 (+18 h)
again an example of a discrete dynamical system study of the stability of stationary points to vary a parameter. Nonlinear systems 2 for 2. Existence of stable and unstable limit cycles
. Policy Bendixon. Criterion for determining whether a flat region is invariant (trapping). Bendixon-Poincare theorem. Various examples and exercises. 
again an example of a discrete dynamical system study of the stability of stationary points to vary a parameter. Nonlinear systems 2 for 2. Existence of stable and unstable limit cycles
. Policy Bendixon. Criterion for determining whether a flat region is invariant (trapping). Bendixon-Poincare theorem. Various examples and exercises.
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Lecture 8, Thursday, April 26, 2007 (+16 h)
Still on mathematical models on a single isolated population. 
Still on mathematical models on a single isolated population.
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Lesson 7, Tuesday, April 24, 2007 (+14 h)
Early examples mathematical models for growth of a single isolated population. Models with predation, removal, addition, etc. 
Early examples mathematical models for growth of a single isolated population. Models with predation, removal, addition, etc.
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Lesson 6 Thursday, April 19, 2007 ( +12 h)
sixth lesson of the course of Mathematical Modeling for Biology. Recent examples and exercises on the method of linearization (and the method of Lyapunov) for the analysis of equilibrium points for nonlinear differential systems 2 for 2. 
sixth lesson of the course of Mathematical Modeling for Biology. Recent examples and exercises on the method of linearization (and the method of Lyapunov) for the analysis of equilibrium points for nonlinear differential systems 2 for 2.
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