Elementary knowledges of calculus in one and several varialbles. Elementary knowledges of linear algebra.
The classes have four components: 1. Theoretical, with an expository character, where one promotes a strong interaction between the concepts and their application. 2. Theoretical and practical, where the student solves problems under the guidance of the teacher. 3. Laboratorial, with (numerical) simulations of the models. 4. Seminar, where the student, under supervision, prepares a written project, presented in a seminar environment.
Qualitative and quantitative study of various biological models.
Discrete and continuous models for the population dynamics, for one or more species: prey/predator, competition, mutualism.
Dynamics of infectious diseases: SIS and SIR models, with and without age-structured population.
Population genetics, and evolution with and without selection. Mutations.
Biological movements: invasion and dispersion.
Pattern formation and chemotaxis: bacteria patterns, and color patterns.
Laboratory work or Field work: 12.5%
Resolution Problems: 25.0%
Oral presentation of the project: 27.5%
Bibliografia de base
A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods. Gerda de Vries, Thomas Hillen, Mark Lewis, Johannes Müller, and Birgitt Schönfisch. SIAM, 2006.
Essential Mathematical Biology. N.F. Britton. Springer 2003.
Mathematical Biology I - An Introduction. J.D. Murray. Springer, 2002.
Modelling biological populations in space and time.
Cambridge Studies in Mathematical Biology, Cambridge Univ. Press, New York, 1993.