# Civil Engineer`s Reference Book by L. S. Blake

By L. S. Blake

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61 with 3 degrees of freedom for the column heading and 8 for the row heading when comparing with the tabulated F values. 59. The observed value does not exceed this and so there is no assertion that can be made at the 1% level. 07. The observed value exceeds this and so a result significant at the 5% level has been obtained. Thus, although there is not strong evidence there is some evidence of a real difference between batches. In an example so small as this one the necessary arithmetic (especially if properly organized) may reasonably be tackled by hand.

2). 3 Maxima and minima Maxima and minima of functions occur when the function has zero slope or first differential. S6 Sy X Sy _ _ = C O s 01 or ^=cos0 ((57) In cases where inverse trigonometric functions are involved, the principle of substitution is employed, for suppose: y = sin ] u we set: d-61) and solve this equation, say * = *,. 4 Integration Integration is generally the reverse of the process of differentiation. It may also be regarded as equivalent to a process of summing a number of finite quantities but, in the limit the number of quantities becomes infinite and their size becomes infinitesimal.

It is to deal with the evaluation of such scattered experimental results that statistical techniques have been developed. It is supposed that, were it possible to continue the experiments indefinitely, the results so obtained would cluster around some fixed value which would be the required value. ) Since it is not possible to conduct indefinitely long experiments the problem becomes that of trying to determine, from a finite series of experiments, that fixed value (which is presumably the true value) about which the indefinite series of results would cluster.