By A. R. Camina, G. J. Janacek (auth.)
With the expansion of recent computing energy it has develop into attainable to use way more arithmetic to actual difficulties. This has resulted in the trouble that many folks who've been operating in a variety of jobs without notice locate themselves now not realizing the fashionable processing that is being utilized to their very own expert box. It additionally signifies that the folks almost immediately being educated in those matters have to comprehend a much broader variety of mathe matics than long ago. it really is to either one of those teams that this booklet is addressed. the key target is to provide the reader with the fundamental mathematical knowing to persist with the hot advancements of their personal box. the math during this e-book relies at the have to comprehend sign procedure ing. the fashionable paintings during this quarter is mathematically very refined and our function isn't to coach specialist mathematicians yet to make way more of the literature obtainable. in view that this booklet is predicated on classes devised for Racal Geophysics there's basically going to be a bias in the direction of the functions in that quarter, because the name implies. it's also actual that the bibliogra phy has been selected to be able to relief the reader in that box by means of pointing them towards fresh purposes in geophysics.
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Extra info for Mathematics for Seismic Data Processing and Interpretation
You will often see ea = f( a) written as b = f( a) = exp( a). It is such an important and useful function that most computer languages have it provided. Power functions can often arise as solutions to equations. Suppose we have a function f(t) where f(t) is some value at time t. Suppose we notice f(t + 1)- f(t) = xf(t) for some value x, so the increment in our time interval is proportional to the function value. If f(O) = I (for simplicity) then f(l) =(1 + x)f(O) =(1 + x) f(2) = (1 + x)f(l) = (1 + xf f(t) giving a power function!
13 4 TAYLOR SERIES AND APPROXIMATIONS Suppose we have the function y = f(x) and we know the value of the function at Xo but that the value of f(x o + h) is not known. One could imagine that f(x) might be sales at time x and that we are trying to extrapolate. If () is the slope of the curve at x o, then an approximation to l>y is h tan () = h dy / dx, see Fig. 13, and so f(xo + h) = f(xo) +h(dY ) dx atx=xo This is a simple but very useful approximation which is the key to Newton's approximation method.
G. J x 2+ l is the distance from the point (x, y) to the origin. The weight of a rectangular sheet of metal of sides x and y with density p is given by pxy. Ifwe use such functions then we shall need ideas like that of the derivative which leads us to the idea of partial derivatives. These ideas are complex, mainly because it is so difficult to visualise the functions involved. If we know then a picture requires the drawing of a 3-dimensional diagram, see Fig. 14. One way round this problem is to draw a contour map, Fig.
Mathematics for Seismic Data Processing and Interpretation by A. R. Camina, G. J. Janacek (auth.)