This curricular unit (CU) aims at providing experience and competencies in converting real-world problems into mathematical equations, in particular, the formulation of problems resulting in partial differential equations.
- be able to formulate a well-posed system of equations from a physical problem;
- be aware of the importance and effects of boundary conditions;
- be familiar with common techniques for simplifying PDEs, for example, separation of variables, similarity
solutions, which result in ODEs, as well as the numerical solution using octave/matlab.
- analyse the resulting equations to find useful properties and solutions;
- interpret properties and solutions in terms of the behaviour of the original problem.
Formulation of well-posed problems, classification of PDEs into elliptic, hypobolic, or parabolic systems, importance of boundary conditions.
Interpretation of mechanical concepts, e.g. conservation of energy and momentum, damping, forcing, steady-states and equilibria, stability in physical systems.
Interpretation, consideration of approximations, accuracy of equations, generalisation of problems, solvability, numerical solutions, e.g. through the use of octave/matlab.
Examples will be taken from (but not limited to) mechanics, mathematical biology, physical and/or chemical systems, traffic flow, reaction-diffusion equations, pattern-formation, coagulation-fragmentation problems, spread of disease, tomography, fluid flow.
A avaliação tem caráter individual e implica a coexistência de duas modalidades: avaliação contínua (60%) e avaliação final (40%). Essa avaliação será desenvolvida na aplicação de formas diversificadas, definidas no Contrato de Aprendizagem da unidade curricular.