Transcription of NumericalDifferentiation andIntegration
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NumericalDifferentiation andIntegration
CHAPTER 11 Numerical Differentiationand IntegrationDifferentiation and integration are basic mathematical operations with a widerange of applications in many areas of science. It is therefore important to havegood methods to compute and manipulate derivatives and integrals. You proba-bly learnt the basic rules of differentiation and integration in school symbolicmethods suitable for pencil-and-paper calculations. These are important, andmost derivatives can be computed this way. Integration however, is different,and most integrals cannot be determined with symbolic methods like the onesyou learnt in complication is the fact that in practical applications a function isonly known at a few points. For example, we may measure the position of acar every minute via a GPS (Global Positioning System) unit, and we want tocompute its speed.
10¡n sin0.5/2 …10¡n0.2397, which is in complete agreement with example 11.3. This is true in general. If f 00 is continuous, then » h will approach a when h
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