Understanding equations

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Geophysicists are often turned off by equations. This is unfortunate because equations are simply compact, quantitative expressions of relationships, and one should make an effort to understand the information that they convey. They tell us what factors are important in a relationship and their relative importance. They also suggest what factors are not relevant, except perhaps through indirect effects on the relevant factors. Graphs often help us visualize equations more clearly. We may think of derivatives as simply measures of the slopes of curves, maxima and minima being merely the places where the slopes are zero, and integration as simply summing up the area under a curve. An imaginary exponential indicates a periodic function. Limitations imposed by initial assumptions or by approximations in their derivations apply to most equations, and these should be appreciated in order to avoid drawing erroneous conclusions from the equations.

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