Loopas said:
A Taylor series is a mathematical representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. It is used to approximate a complex function with a simpler polynomial function, making it easier to work with.
The purpose of a Taylor series is to approximate a complex function with a simpler polynomial function, allowing for easier calculations and analysis. It can also be used to find the value of a function at a point where the original function is not defined.
A Taylor series is calculated by taking derivatives of a function at a specific point and plugging them into a formula that involves the function's value at that point. The more derivatives that are included in the calculation, the more accurate the Taylor series approximation will be.
In direct differentiation, the derivatives of a function are explicitly calculated and used in the Taylor series formula. In non-direct differentiation, the derivatives are not explicitly calculated, but are found by using other methods such as integration or power series expansion.
A Taylor series can be used for non-direct differentiation by finding the derivatives of a function using other methods such as integration or power series expansion, and then plugging those derivatives into the Taylor series formula. This allows for more complex functions to be approximated with a Taylor series.
