Mathematics and the environment
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. However, the
course does require the willingness to become familiar with a range of
different scientific disciplines. In particular, familiarity with the
concepts of fluid mechanics will be useful.
Applications of mathematics to environmental or geophysical problems
involving the use of models with ordinary and partial differential
equations. Examples to be considered are:
River flow and sediment transport.
A. C. Fowler 2004 Mathematics and the environment. Mathematical
Institute lecture notes. (Revised edition, September 2006.)
K. Richards 1982 Rivers. Methuen.
G. B. Whitham 1974 Linear and nonlinear waves. Wiley, New York.
W. S. B. Paterson 1994 The physics of glaciers, 3rd edition. Pergamon
J. T. Houghton 2002 The physics of atmospheres, 3rd ed. C.U.P., Cambridge.
(Page numbers refer to the printed lecture notes.) (Updated
- Radiative heat transfer (pp. 3-17).
- Convection (pp. 17-19).
- Energy balance models (pp. 20-29).
- Ice ages (pp. 29-42).
- Chézy and Manning flow laws (pp. 66-70).
- Slowly varying flow; flood hydrograph (pp. 70-72).
- Rapidly varying flow, St. Venant equations (pp. 72-76).
- Waves and instability (pp. 77-88).
- Patterns and bedforms (pp. 103-107).
- Bedload transport; the Exner equation. Suspended
sediment. Potential flow model.
- St. Venant type models (pp. 113-118).
- Anti-dunes and dunes (pp. 119-129).
- Waves and surges (pp. 156-164, 186-188).
- Surface waves. Subglacial sliding (pp. 164-168, 180-184).
- Subglacial drainage (pp. 184-185).
- Linked cavity systems and surges (pp. 188-194).
These can be downloaded as pdf files; currently available are
Lecture notes, pdf, as of
6/10/06. These contain chapters on climate,
river flow, sediment transport and glacier flow. Some parts of the
chapters are still uncompleted.
- Article on 'Glaciers' (pdf
file), from the
Encyclopedia of Atmospheric Sciences, Elsevier (2003).
- Problem sheets pdf as at 31/10/06. These have now
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