ANM06001 Differential Equations

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Integrated Arts and Sciences Department of Integrated Arts and Sciences

Lecture Code ANM06001 Subject Classification Specialized Education

Subject Name 微分方程式

Subject Name
（Katakana）ビブンホウテイシキ

Subject Name in
English Differential Equations

Instructor KOBAYASHI RYO

Instructor
(Katakana) コバヤシ　リョウ

Campus Higashi-Hiroshima Semester/Term 2nd-Year, First Semester, 2Term

Days, Periods, and Classrooms (2T) Tues1-4：IAS C808

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Face-to-face instruction.
Practical sessions (Python) in parallel.

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Differential equations, Modeling, Simulation

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Differential equations constitute a powerful mathematical language for describing natural and social phenomena. Through modeling with differential equations, students will understand the mathematical structures governing phenomena and learn how such models can be used to predict and control them. This perspective provides an important foundation for research themes within the Integrated Sciences Program.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Integrated Arts and Sciences
（Knowledge and Understanding）
・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework.
（Abilities and Skills）
・The ability and skills to specify necessary theories and methods for consideration of issues.

Class Objectives
/Class Outline The course aims to provide the theoretical foundations of ordinary differential equations while developing an understanding of solution behavior through numerical computation. Furthermore, students will acquire the ability to formulate real-world phenomena as mathematical models.

Class Schedule What is a differential equation? / What does it mean to solve a differential equation?
The equation of radioactive decay
Introduction to numerical computation
Separable differential equations
Malthusian model and the logistic equation
Models of chemical reaction systems
Models of infectious diseases / SIR model
Discrete equations for diffusion phenomena (n-box system)
Second-order linear differential equations:
Harmonic oscillator, spring–mass–damper systems, LCR circuits, resonance phenomena
Equations of motion of a particle / motion of a pendulum and celestial bodies
Equilibrium points, stability, and bifurcation
Limit cycles / van der Pol equation
Chaos / Lorenz equations
Each 180-minute class session will consist of theoretical introduction and analytical treatment in the first half, followed by simulation practice and modeling exercises in the second half.
Learning techniques to be incorporated:
Based on sample programs, students will perform numerical computations and visualize solutions for various model equations, thereby acquiring practical simulation techniques.

A final examination will be conducted after the last class session.

This course will be delivered by Professor Ryo Kobayashi, Professor Emeritus of Hiroshima University.

Text/Reference
Books,etc. Textbook: None specified.
References:
1) Masahiro Kaminaga, Learning Differential Equations with Python and Practical Examples, Corona Publishing.
2) David Burgess and Morag Borrie, Creating Mathematical Models with Differential Equations, Nippon Hyoron Sha.

PC or AV used in
Class,etc. Other (see [More Details])

(More Details) https://www.mls.sci.hiroshima-u.ac.jp/ryo/Differential_Equation/index.php
Google Colab; students’ own laptop computers.

Learning techniques to be incorporated

Suggestions on
Preparation and
Review By engaging with differential equations through numerical computation, students are encouraged to develop an intuitive understanding of their properties.

Requirements Completion of Calculus I is recommended. However, students who understand high school–level calculus and vectors may also enroll.

Grading Method Evaluation will be based on examinations and reports.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2026Year	School/Graduate School	School of Integrated Arts and Sciences Department of Integrated Arts and Sciences
Lecture Code	ANM06001	Subject Classification	Specialized Education
Subject Name	微分方程式
Subject Name （Katakana）	ビブンホウテイシキ
Subject Name in English	Differential Equations
Instructor	KOBAYASHI RYO
Instructor (Katakana)	コバヤシ　リョウ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues1-4：IAS C808
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Face-to-face instruction. Practical sessions (Python) in parallel.
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Differential equations, Modeling, Simulation
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Differential equations constitute a powerful mathematical language for describing natural and social phenomena. Through modeling with differential equations, students will understand the mathematical structures governing phenomena and learn how such models can be used to predict and control them. This perspective provides an important foundation for research themes within the Integrated Sciences Program.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Integrated Arts and Sciences （Knowledge and Understanding）・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework. （Abilities and Skills）・The ability and skills to specify necessary theories and methods for consideration of issues.
Class Objectives /Class Outline	The course aims to provide the theoretical foundations of ordinary differential equations while developing an understanding of solution behavior through numerical computation. Furthermore, students will acquire the ability to formulate real-world phenomena as mathematical models.
Class Schedule	What is a differential equation? / What does it mean to solve a differential equation? The equation of radioactive decay Introduction to numerical computation Separable differential equations Malthusian model and the logistic equation Models of chemical reaction systems Models of infectious diseases / SIR model Discrete equations for diffusion phenomena (n-box system) Second-order linear differential equations: Harmonic oscillator, spring–mass–damper systems, LCR circuits, resonance phenomena Equations of motion of a particle / motion of a pendulum and celestial bodies Equilibrium points, stability, and bifurcation Limit cycles / van der Pol equation Chaos / Lorenz equations Each 180-minute class session will consist of theoretical introduction and analytical treatment in the first half, followed by simulation practice and modeling exercises in the second half. Learning techniques to be incorporated: Based on sample programs, students will perform numerical computations and visualize solutions for various model equations, thereby acquiring practical simulation techniques. A final examination will be conducted after the last class session. This course will be delivered by Professor Ryo Kobayashi, Professor Emeritus of Hiroshima University.
Text/Reference Books,etc.	Textbook: None specified. References: 1) Masahiro Kaminaga, Learning Differential Equations with Python and Practical Examples, Corona Publishing. 2) David Burgess and Morag Borrie, Creating Mathematical Models with Differential Equations, Nippon Hyoron Sha.
PC or AV used in Class,etc.	Other (see [More Details])
(More Details)	https://www.mls.sci.hiroshima-u.ac.jp/ryo/Differential_Equation/index.php Google Colab; students’ own laptop computers.
Learning techniques to be incorporated
Suggestions on Preparation and Review	By engaging with differential equations through numerical computation, students are encouraged to develop an intuitive understanding of their properties.
Requirements	Completion of Calculus I is recommended. However, students who understand high school–level calculus and vectors may also enroll.
Grading Method	Evaluation will be based on examinations and reports.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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