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Mathematical Modelling for Earth Sciences

Xin-She Yang

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17 Apr 2008
Dunedin Academic Press
272 pages - 234 x 156 x 23mm
Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental, and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Author Xin-She Yang has carefully selected the topics which will be of most value to students. Dr. Yang has recognized the need to be careful in his examples while being comprehensive enough to include important topics and popular algorithms. The book is designed to be 'theorem-free' while balancing formality and practicality. Using worked examples and tackling each problem in a step-by-step manner, the text is especially suitable for more advanced students of this aspect of earth sciences.
I Mathematical Methods 1. Mathematical Modelling; 2. Calculus and Complex Variables; 3. Vectors and Matrices; 4. ODEs and Integral Transforms; 5. PDEs and Solution Techniques; 6. Calculus of Variations; 7. Probability; 8. Geostatistics; II Numerical Algorithms. 9. Numerical Integration; 10. Finite Difference Method; 11. Finite Volume Method; 12. Finite Element Method; III Applications to Earth Sciences. 13. Reaction-Diffusion System; 14. Elasticity and Poroelasticity; 15. Flow in Porous Media. A. Mathematical Formulae. B. Matlab and Octave Programs. Bibliography. Index.
Xin-She Yang received his DPhil in applied mathematics from the University of Oxford, he is currently a research fellow at the University of Cambridge.

'Quantitative methods are increasingly important in the earth sciences but there are few good books specifically written to help earth scientists develop the mathematical tools that they need. This book helps to fill the gap by providing a concise introduction to mathematical modelling with an emphasis on examples taken from the earth sciences.

One of the major strengths of the book is that it is possible to get a good overview of a whole topic during an initial read of the relevant chapter without getting too bogged down in detail. Where additional detail is provided it is invariably worth further study. Another strength of the book is the large number of worked examples embedded in the text – almost every other double-page spread seems to have one. With very few exceptions, these examples are of great help in providing both focus and clarity to what may sometimes seem a little obscure. The style of the book is informal - I wish that it had been available when I was an undergraduate to help counterbalance the “theorem-and-proof” approach that I was subjected to...
In short, the book provides excellent value for money and is a well-crafted introduction to mathematical modelling for earth scientists. Armed with insights obtained from this book, the reader will be well placed for further study of selected topics at the next level of detail.'Geoscientist

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