Forest managers are interested in measures of how crowded a given forest stand is.† One measurement used is the stand-density index, or SDI. It can be related to the number N of trees per acre and the diameter D, in inches, of a tree of average size (in terms of cross-sectional area at breast height) for the stand. The relation is given below. log(SDI) = log(N) + 1.605 log(D) − 1.605 (a) A stand has 450 trees per acre, and the diameter of a tree of average size is 5 inches. What is the stand-density index? (Round your answer to nearest whole number.) (b) What is the effect on the stand-density index of increasing the number of trees per acre by a factor of 10, assuming that the average size of a tree remains the same? The SDI will increase by a factor of       . (c) What is the relationship between the stand-density index and the number N of trees per acre if the diameter of a tree of average size is 10 inches? SDI =

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.