# C5.11 Mathematical Geoscience - Material for the year 2019-2020

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, familiarity with the concepts of fluid mechanics will be useful.

Students will have developed a sound knowledge of some of the models studied in mathematical geoscience. They will also get exposure to some modern research topics in the field.

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).