Numerical Methods Using Java: For Data Science, Analysis, and Engineering

© Haksun Li, PhD 2022

H. Li, PhDNumerical Methods Using Javahttps://doi.org/10.1007/978-1-4842-6797-4_6

6. Numerical Differentiation and Integration

Haksun Li, PhD¹  

(1)

Hong Kong, China

 

Numerical differentiation and integration is a technique to do differentiation and integration when we do not know the function a priori, when we treat the function as a black box, or when analytical (or symbolic or closed-form) differentiation and integration of the function is not possible. The technique approximates a function by many linear functions, each on a tiny interval of the function domain. In fact, piecewise linear approximation of a function is the very foundation of calculus. When the intervals are small enough or when we zoom in the function enough, ...