![]() ![]() In this post, the Python implementation, along with some potential uses for the Taylor series are discussed and presented. ![]() This implementation requires only the definition of the function being approximated, the rest is handled numerically. Recently, while studying for the GRE Mathematics Subject Test, I developed a deeper appreciation for the Taylor series and decided to implement them in Python. When first confronted with the Taylor series while working on my undergraduate degrees, they seemed like just another thing. However, there aren’t many that show why we should really care. ![]() Many posts about the Taylor series (and some YouTube videos) help build an intuition for the infinite series by showing how higher-order terms provide ever closer approximations of the underlying function (provided the series converges). More accurate approximations can be determined by taking higher-order derivatives and using higher degree polynomials. The Taylor series of a function is an infinite sum of terms that uses information about the derivative of the function to create a polynomial that approximates the function. ![]()
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