By John Ferguson (auth.)
1. 1 resolution of geological problems-are mathematical equipment helpful? a question that is usually requested is whether or not it will be important for geologists to understand and to take advantage of arithmetic within the preparation in their technological know-how. there is not any easy resolution to this question, and it really is real that many geologists have had winning careers with out ever desiring to become involved in something except uncomplicated arithmetic, and the entire symptoms are that this is often more likely to proceed into the long run. even though, in lots of branches of the topic the fad has been in the direction of utilizing a numerical method for the answer of appropriate difficulties. the level to which this happens is dependent upon the character of the realm being studied; hence, in structural geology, that is con cerned in its easiest elements with the geometrical relationships among quite a few positive factors, there are numerous difficulties that are simply solved. extra lately using analytical equipment has allowed the answer of more-difficult difficulties. In one other region, geochemistry, issues have occurred. at the theoretical aspect there was a better integration with actual chemistry, which itself is a hugely mathematical topic; and at the functional part there's the necessity to examine and interpret the gigantic amounts of information which modem instrumentation produces. inside geology the appliance of numerical equipment has been given quite a few names, so now we have numerical geology, geo arithmetic, geostatistics and geosimulation.
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Additional info for Mathematics in Geology
2 number of equally likely favourable outcomes total number of equally likely possible outcomes Multiplication axiom If two events £ 1 and £ 2 are independent, such that the outcome of one does not affect the outcome of the other, then the probability that both £ 1 and £ 2 happen is the product of their individual probabilities: In general, p(E1 and £ 2 and ... and En) = fJ p(E;) i=l Note the use here, as elsewhere in this book, of the symbol fl, which is the conventional shorthand for multiplication.
This is the imaginary unit denoted by the symbol i, hence the sum of a real and imaginary number is referred to as a complex number. The solution to the quadratic equation, the roots given above are, therefore, complex numbers. A complex number whose imaginary part is equal to zero is a real number. As with other numbers, there are rules of representation and manipulation for complex numbers. These are not dealt with here, since most geological problems have real solutions. 1. 7 Linear programming Linear programming is a method of finding the best solution to a problem in maximization (or minimization), in the presence of constraints.
The equations are obtained by calculating a line of best fit using a least-squares method. In geological simulations quadratic equations have also been used combined with other functions, for beach profiles (Fox & Davis 1971). In both of these applications the numerical value y (the dependent variable) is the height of the profile above some suitable datum level, at a point at a distance x (the independent variable) from an origin measured along the datum. + bx+ c Of particular significance, as we shall see later, are values of x when 27 ALGEBRA y = 0, which are known as the roots of the equation.