Basic mathematical processes like differentiation and integration have numerous applications in a variety of scientific fields. It is crucial to have accurate computation and manipulation techniques for derivatives and integrals. The fundamentals of differentiation and integration—symbolic procedures appropriate for computations on paper and with a pencil—were likely taught to you in school. Most derivatives can be calculated using this method, and they are crucial. However, integration is different, and the majority of integrals cannot be calculated using the symbolic techniques you learned in school.

The fact that a function is only known at a few locations in real applications adds further complexity. For instance, we may use a GPS (Global Positioning System) device to track the position of an automobile every minute and wish to determine its speed. If we know the location as a continuous function of time, we may differentiate this function to get the speed. However, this is impossible if the location is only known sometimes. Integrals follow the same rules. Utilizing approximate methods of differentiation and integration is the answer for both functions that can only be known at discrete locations and integrals that cannot be computed by conventional methods. In our context, these are going to be numerical methods.

In this “Numerical Differentiation and Integration - Numerical Methods” you will learn about the following topics:

1. Newton's differentiation formulas
3. Trapezoidal and Simpson’s Rules
4. Gaussian integration algorithm
5. Romberg integration formulas

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This article Numerical Differentiation and Integration - Numerical Methods is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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