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

神田 学(著)/バルケズ アルビン(訳)

神田 学(著)/バルケズ アルビン(訳)

定価 3,520 円(本体 3,200 円+税)

ISBN:978-4-254-20169-7 C3050

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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


The sample codes are available from the download link in the right side of this page.


1. Overview
1.1 Ordinary differential equations as an engineering language
1.2 Very basic Python tutorial

2. 1st order ODE
2.1 Variable separation method
2.2 Variable separation of 1st derivatives of linear expresssion
2.3 1st order non-linear ODE solvable by variable separation
2.4 Exercise 1

3. 2nd order linear ODE
3.1 Methodtoderivingan exact solution
3.2 Mass–spring system.
3.3 Behavior of current flowing in an RCL circuit
3.4 Disk rotation subjected to tortion and resistance
3.5 Deriving the law of conservation of energy using the law of
conservation of momentum
3.6 Exercise 2

4. 2nd order linear non-homogeneous ODE
4.1 Derivingthe exact solution
4.2 Behavior of mass–spring system with periodic external force
4.3 Behavior of current in RLC electric circuit with AC voltage
4.4 Exercise 3

5. Numerics for ODEs
5.1 Basic concept of the solution
5.2 Eulermethod
5.3 4th order Runge–Kutta
5.4 Numerical solution of multiple simultaneous 1st order ODEs
5.5 Numerical solution of n-order ODEs
5.6 Exercise 4

6. ODE and Chaos
6.1 Non-linearmass–spring systemand chaos
6.2 Physical definition and characteristics of chaos
6.3 Characteristics of chaos in the non-linear mass–spring system
6.4 Foodchainand chaos
6.5 Exercise 5

Answers to Problems

A List of formulae
A.1 Trigonometric identites
A.2 Differentiation and integration formulae


神田 学 Manabu Kanda
東京工業大学環境・社会理工学院 教授

アルビン・バルケズ Alvin C. G. Varquez
東京工業大学環境・社会理工学院 教授




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