Mathematics in Geology - John Ferguson

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Résumé :
1. 1 Solution of geological problems-are mathematical methods necessary? A question which is often asked is whether it is necessary for geologists to know and to use mathematics in the practise of their science. There is no simple answer to this question, and it is true that many geologists have had successful careers without ever needing to get involved in anything other than simple mathematics, and all the indications are that this is likely to continue into the future. However, in many branches of the subject the trend has been towards using a numerical approach for the solution of suitable problems. The extent to which this occurs depends on the nature of the area being studied; thus, in structural geology, which is con? cerned in its simplest aspects with the geometrical relationships between various features, there are many problems which are easily solved. More recently the use of analytical methods has allowed the solution of more-difficult problems. In another area, geochemistry, two things have happened. On the theoretical side there has been a greater integration with physical chemistry, which itself is a highly mathematical subject; and on the practical side there is the need to analyse and interpret the vast quantities of data which modem instrumentation produces. Within geology the application of numerical methods has been given various names, so we have numerical geology, geo? mathematics, geostatistics and geosimulation.

Sommaire:
1 Introduction.- 2 Useful mathematical ideas.- 3 Sequences and series.- 4 Rates of change - differentiation.- 5 Areas and volumes: integration.- 6 Number arrays, the algebra of matrices.- 7 Introduction to numerical methods.- 8 Geological applications of differential equations.- 9 Beyond traditional mathematics.- Appendix 1 An introduction to the methods of differentiation.- A1.1 The rules of differentiation and their application.- A1.2 Standard forms and their use.- A1.3 Implicit differentiation.- Appendix 2 An introduction to the methods of integration.- A2.1 The rules of integration.- A2.2 Standard forms.- A2.3 Substitution.- Appendix 3 Computer programs.- References.