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Nonlinear Dynamics & Chaos Theory

Course Co-ordinator: Marco Thiel

Pre-requisite(s): A BSc Hons at class 2.2 or above in a science subject.

This course covers the fundamental mathematical concepts required for the description of dynamical systems, i.e. systems that change in time. It discussed nonlinear systems, for which typically no analytical solutions can be found: these systems are pivotal for the description of natural systems in physics, engineering, biology etc. Some emphasis will be on the study of chaotic systems and strange, i.e. fractal attractors.
Next to the theory of relativity and quantum mechanics, chaos and dynamical systems theory is being considered as one of three major advances in the natural sciences. This course covers the mathematics behind this paradigm changing theory.

2 one-hour lectures and one-hour tutorial (to be arranged).

1st attempt: 1 two-hour written examination (50%); continuous assessment (50%).

Resit: Written exam (100%).

Modelling Theory

Course Co-ordinator: Marco Thiel

Pre-requisite(s): A BSc Hons 2.2 class or above in a science subject.

Physical Sciences intend to describe natural phenomena in mathematical terms. This course bridges the gap between standard courses in physical sciences, where successful mathematical models are described, and scientific research, where new mathematical models have to be developed. Students will learn the art of mathematical modelling, which will enable them to develop new mathematical models for the description of natural systems. Examples from a wide range of phenomena will be discussed, e.g. from biology, ecology, engineering, physics, physiology and psychology.
A focus will be the critical interpretation of the mathematical models and their predictions. The applicability of the models will be assessed and their use for the respective branch of the natural sciences will be discussed.

2 one-hour lectures, 1 one-hour computer lab/lecture, and 1 one-hour tutorial per week.

1st attempt: Continuous assessment (assignments & projects: 80%); oral exam (20%).

Resit: Mini modelling project (80%); oral exam (20%).