1. An Introduction to Mathematical Biomedicine Rolando Placeres Jiménez Departamento de Física, Universidade Federal de São Carlos, Brazil. Ceramic Laboratory, École Polytechnique Federal de Lausanne, Switzerland. rplaceres@df.ufscar.brrplaceres@df.ufscar.br and roland.placeres@epfl.chroland.placeres@epfl.ch

2. Continuous processes and ordinary differential equations 1.Introduction: Growth of microorganism. 2.Stability and linearization. 3.Nonlinear dynamics. 4.Single specie model and multiple specie model: Exponential growth, Logistic growth, Gompertz, and Lotka-Volterra. 5.Competitive Lotka-Volterra model.

9. Phase plane diagrams of linear systems

15. Nonlinear dynamics An attribute of two-dimensional systems that is not share by those of higher dimensions is that local behavior at steady state can be used to reconstruct global behavior. Bigger systems can not be treated in the same way, high dimensional systems are less constrained and trajectories can be more complex than in two-dimensional systems.

32. Bibliography 1.L. Edelstein-Keshet. Mathematical Models in Biology (SIAM, New York, 2005). 2.F. Brauer, C. Castillo-Chavez. Mathematical models in population biology and epidemiology (Springer-Verlag, Berlin, 2010).

33. Thanks!