A Taylor Series is a mathematical tool used to approximate complex functions using polynomials. It expresses a function as an infinite sum of terms calculated from the function's derivatives at a single point. This allows for easier calculations and analysis of functions that may be difficult to work with directly.
The series is named after the mathematician Brook Taylor, who introduced it in the early 18th century. A common application of the Taylor Series is in calculus, where it helps in estimating values of functions like sin(x) or e^x near a specific point, making it invaluable in both theoretical and applied mathematics.