# C5.11 Mathematical Geoscience - Material for the year 2020-2021

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*B5.2 Applied Partial Differential Equations* and *B5.3 Viscous Flow* recommended.

16 lectures

### Assessment type:

- Written Examination

The aim of the course is to illustrate the techniques of mathematical modelling in their particular application to environmental problems. The mathematical techniques used are drawn from the theory of ordinary differential equations and partial differential equations. The course requires a willingness to become familiar with a range of different scientific disciplines. In particular, some familiarity with the concepts of fluid mechanics will be useful. The course will provide exposure to some current research topics.

Students will be able to:

- Derive and explain mathematical models for a range of geoscientific problems
- Analyse such models to determine the relative importance of different physical and chemical effects, and to formulate appropriate reduced models
- Use a range of mathematical techniques to solve the models, and be able to interpret the results in terms of applications to real-world phenomena

Applications of mathematics to environmental or geophysical problems involving the use of models with ordinary and partial differential equations. Examples to be considered are:

- Climate dynamics (radiative balance, greenhouse effect, ice-albedo feedback, carbon cycle)

- River flows (conservation laws, flood hydrographs, St Venant equations, sediment transport, bed instabilities)

- Ice dynamics (glaciers, ice sheets, sea ice)

- A. C. Fowler,
*Mathematical Geoscience*(Springer, 2011). - J. T. Houghton,
*The Physics of Atmospheres*(3rd ed., Cambridge University Press., Cambridge, 2002). - K. Richards,
*Rivers*(Methuen, 1982). - K. M. Cuffey and W. S. B. Paterson,
*The Physics of Glaciers*(4th edition, Butterworth-Heinemann, 2011).