Differentiation
There are three ways to approach the computation of derivatives:
- Numerical differentiation refers to the process of approximation of the derivative of a given function at a point. In SciPy, we have the following procedures, which will be covered in detail:
- For generic univariate functions, the central difference formula with fixed spacing.
- It is always possible to perform numerical differentiation via Cauchy's theorem, which transforms the derivative into a definite integral. This integral is then treated with the techniques of numerical integration explained in the upcoming section.
- Symbolic differentiation refers to computation of functional expressions of derivatives of functions, pretty much in the same way that we would do manually. It is termed symbolic because unlike its numerical counterpart, symbols take the role of variables, rather than numbers or vectors of numbers. To perform symbolic differentiation, we require a computer algebra system (CAS), and in the SciPy...
