We aim to provide an introduction to important methods and examples of determinstic and stochastic mathematical modeling based on differential and difference equations. Many examples will be discussed, taken from diverse domains of applications, from Natural Science (Physics, Chemistry, Biology) to Engineering, and Social Science. A particular focus will be generic behavior induced by the nonlinear nature of the models studied, such as deterministic chaos, pattern formation. and other. As more specific objectives, we can highlight:
- To be able to formulate a practical model in terms of conservation and constitutive laws, in a consistent way from the point of view of physical dimensions, identifying the main dimensional constants and dimensionless constant ratios characterizing it.
- To become familiar with paradigmatic modeling approaches in Science, Engineering, and Socioeconomic systems through ordinary differential equations, discrete maps, and partial differential equations.
- To become familiar with discrete or continuous-time stochastic models provided by important Markov processes.
- To have a working knowledge of the qualitative theory of dynamical systems.
- To get acquainted with bifurcation phenomena in low-dimensional dynamical systems and partial differential equations.
- To be able to identify and characterize chaotic behavior in discrete and continuous low-dimensional deterministic systems.
- To be acquainted with further nonlinear phenomena in spatially-extended systems, such as reaction-diffusion processes, wave behavior, or pattern formation.
Basic competences: CB6, CB7, CB8, CB9, CB10
General competences: CG1, CG2, CG3, CG4, CG5, CG6, CG7
Specific competences: CE1, CE2, CE3, CE4, CE5, CE6, CE7, CE8, CE9, C11