Function Analysis: How it works
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Description How it works Examples: Reaction Kinetics 1-D Random Walk Analysis of Noisy Data |
The function uses Excel's Data Table feature to calculate the values of the function at thousand points between the minimum and maximum values specified. The defined formula 'dx' calculates the step size, and the defined name 'x' is used so that the user can enter a function in terms of x, as done conventionally.  The X and Y values for the function plot are evaluated in columns X and Y respectively using the Data Table. The values are rounded off to 5 places. The algorithms used to calculate the derivative and the integral are the central difference method (3 point formula) and Trapezoidal rule respectively. These are done in columns Z and AA. These algorithms have an error of the order O(h2). As long as the range of evaluation is not very large, the use of these algorithms will give us results close to the actual values.  (To switch to formula view in Excel, press CTRL and ` keys. Press the same keys again to get back to the normal view.) Do bear in mind that numerical methods have limitations and these must be kept in mind while using them or while interpreting the results obtained from them. Read this wiki page on numerical methods for an overview. |