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| 1.2 Numerical Methods (Module I) |
| We encounter the first application of a numerical method when we fit the “best” curve or a straight line passing through a number of experimental data points. When a large number of data points are generated in an experiment, a compact way of dealing with these is through “best” fitting functions or interpolating polynomials. These functions and polynomials have the additional advantage of being amenable to differentiation and integration which are usually the requirement of a physico-chemical problem. A crucial requirement in all these problems is the ability to write/modify computer programs to suit one’s own needs. While this is not a course on computer programming, some chapters are devoted to it so that a serious developer can take up other courses to enhance her skills. In applications of “theoretical” methods to solve chemical problems, good programming skills are very useful. A lot of work that has gone in developing public domain and commercial softwares. While the early programming languages were Basic or Fortran, the present languages in use are C++ or Java and these too will change with time. with time. Often, the ability and to switch from one language to another, while a bit unpleasant, is not very difficult. The programming details are given in Chapter 2. |
There are several methods for interpolation such as the Newton’s forward difference form or the Lagrange interpolation scheme, Newton’s method has an advantage that it is more readily adaptable to schemes for differentiation and integration. The main requirement is the availability of data points at regular intervals. Curve fitting is to be used only if there is significant error in the experimental data points (Chapter 3). |
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