A Reflection of Euler’s Constant and Its Applications

One of the most fascinating and remarkable formulas existing in mathematics is the Euler Formula. It was formulated in 1740, constituting the main factor to reason why humankind can advance in science and mathematics. Accordingly, this research will continue investigating the potentiality of the Euler Formula or "the magical number e." The goal of the present study is to further assess the Euler formula and several of its applications such as the compound interest problem, complex numbers, trigonometry, signals (electrical engineering), and Ordinary Differential Equations. To accomplish this goal, the Euler Formula will be entered into the MATLAB software to obtain several plots representing the above applications. The importance of this study in mathematics and engineering will be discussed, and a case study on a polluted lake will be formulated.