The Taylor Series and Its Application

Abstract

Taylor series, a fundamental concept in mathematics, expresses a function as an infinite sum of terms which is calculated from the values of its derivatives at a single point. Its applications span various fields, notably physics and finance, where it simplifies complex functions for analysis and problem-solving. This study employs a qualitative approach, reviewing existing literature on Taylor series applications. It analyzes case studies in physics, such as approximating motion equations, and in finance, like option pricing models. The method includes mathematical derivations and simulations to demonstrate efficacy. Findings indicate that Taylor series significantly enhance computational efficiency and accuracy. In physics, it aids in predicting particle behavior under varying forces. In finance, it provides valuable insights into the pricing of derivatives and risk assessment. The Taylor series proves to be an indispensable tool in both physics and finance, facilitating complex calculations and improving analytical capabilities. Its versatility underscores the importance of mathematical foundations in real-world applications.