Mathematical Modelling II

Mathematical Modelling II

Cod: 23032

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 260

Total contact time: 10

Total contact time: 10

Mathematical modelling

Differential Equations

Well-Posed Problems

Differential Equations

Well-Posed Problems

- 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.

- 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.

- Fulford, Broadbridge: Industrial mathematics, Cambridge UP, 2002

- Howison: Practical applied mathematics: modelling, analysis, approximation, Cambridge UP, 2005

- Tayler: Mathematical models in applied mechanics, Oxford UP, 2001

- Howison: Practical applied mathematics: modelling, analysis, approximation, Cambridge UP, 2005

- Tayler: Mathematical models in applied mechanics, Oxford UP, 2001

E-learning

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.