Ordinary Differential Equations and Physical Phenomena ―A Short Introduction with Python―

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). ■ 全編英語の常微分方程式(ODE)の教科書。自然現象の数理モデルの例とともに常微分方程式の解法とPythonを使った数値計算法を学ぶ。〔内容〕1st Order ODE／2nd Order ODE／Numerics for ODEs／ODE and Chaos