Understanding Euler's Formula through its Derivation
Video Available Hello. I am going to tell you how to intuitively understand Euler's formula through its derivation. I presume that you understand the concept of Taylor series expansion. If not, please visit the video or the text entitled "The Simplest Way to Understand the Concept of Taylor Series Expansion" before reading this text. Look at this beautiful equation. This is called Euler's formula. It relates the three different mathematical concepts: exponential function, imaginary number and trigonometric functions. If you substitute , then we get This one connects exponential function, imaginary number and pi. The most important point of Euler's formula is that the term plays an important role in science and engineering as the "oscillation kernel." Ok. Let's derive Euler's formula by applying the Taylor series expansion at to . Recall Taylor series expansion at is where Keep in mind that the derivative of exponential functio...