Transdisciplinary Science and Engineering News
After five years since introducing the undergraduate English course entitled, “Ordinary Differential Equations and Physical Phenomena”, a textbook by Prof. Manabu Kanda with translation by Alvin C.G. Varquez is now available for engineering students. The main purpose of the textbook is for readers to appreciate and understand the importance of differential equations in science and engineering. The textbook is an updated version and translation of the Japanese textbook（神田学、常微分方程式と物理現象、朝倉書店） written by Prof. Manabu Kanda in 2012.
The 160-page textbook is concisely designed for engineering and science students who are taking up courses on ordinary differential equations. It assists in self-study, review, and lecture instruction (covering up to 14 lecture sessions in total). An introduction to differential equations and their types are covered in the first chapter. The following chapters, then, focus on each type of ordinary differential equations (ODE), beginning with first-order linear ODEs and ending with higher-order non-linear ODEs. To solve non-linear ODEs, numerical solutions such as the Runge-Kutta methods are also included.
Each chapter contains programming exercises with the Python language. This teaches the readers to model, visualize, and interpret the behavior of each physical phenomenon represented by the ODE and its solution. Various physical phenomena include vibrating springs, electrical circuits, Beer’s law, logistic model, food webs, and chaos (e.g. Butterfly Effect).
Our universe is bounded by certain physical laws that are well known or yet to be uncovered. These laws are represented in mathematical terms; specifically, through differential equations. The textbook encourages readers to appreciate ODE as a communication tool for bridging seemingly different yet essential scientific and engineering fields.