Mathematical Modelling I

Mathematical Modelling I

Cod: 23026

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 260

Total contact time: 10

Total contact time: 10

This unit aims to provide a working knowledge in some mathematical modelling methods, with emphasis in applications to biological contexts.

Mathematical Modelling

Biomathematics

Biomathematics

Upon the conclusion of this LU the student should:

- know the aims and philosophical foundations of modelling in applied sciences, and understand its limitations and usage;

- be able to formulate, nondimensionalise, and study both analytically and by using computer-based tools, models from different biological contexts (ecology, evolution, physiology, biochemistry) using the frameworks of deterministic and stochastic differential, difference , and delay differential equations as appropriate.

- know the aims and philosophical foundations of modelling in applied sciences, and understand its limitations and usage;

- be able to formulate, nondimensionalise, and study both analytically and by using computer-based tools, models from different biological contexts (ecology, evolution, physiology, biochemistry) using the frameworks of deterministic and stochastic differential, difference , and delay differential equations as appropriate.

1) Biological background: kinetics of enzymatic reactions, mathematical ecology, some notions of cell and molecular biology;

2) Modelling using Ordinary Differential Equations in biochemical kinetics; Quasi-steady state assumption and its validity;

3) Dealing with stochasticity: Gillespie's algorithm;

4) Modelling in physiology using delay-differential equations;

5) Modelling in mathematical ecology in discrete time: structured populations and methods of linear algebra;

6) Modelling evolution.

2) Modelling using Ordinary Differential Equations in biochemical kinetics; Quasi-steady state assumption and its validity;

3) Dealing with stochasticity: Gillespie's algorithm;

4) Modelling in physiology using delay-differential equations;

5) Modelling in mathematical ecology in discrete time: structured populations and methods of linear algebra;

6) Modelling evolution.

• Cushing: An Introduction to Structured Population Dynamics, Society for Industrial and Applied Mathematics, 1998

• Erneux: Applied Delay Differential Equations, Springer, 2008

• Murray: Mathematical Biology, 2nd ed. Vols. 1 & 2, Springer, 1993

• Erneux: Applied Delay Differential Equations, Springer, 2008

• Murray: Mathematical Biology, 2nd ed. Vols. 1 & 2, Springer, 1993

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.

This Learning Unit will be taught in English.