Course title
3300870V1
Differential Equations

 ZHAI GUISHENG
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・1 研究者・技術者としての基礎的素養
代数、幾何、解析、応用数学、情報数学などの専門知識を修得し、課題を抽象化して数理的な問題設定をすると共に、適切な理論的考察・計算的手法を用いて問題解決策を構築できる。
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
Natural phenomena can be modeled in terms of differential equations. The most of such equations are nonlinear. We can regard a nonlinear equation as a linear equation by approximating the solution locally. In this class, we will learn how to solve linear differential equations and nonlinear differential equations which can be reduced to the linear one.
Course description
Differential equations are used in describing phenomena and motions in various sciences, and especially in the field of science and engineering, their analysis is indispensable. In recent years, computers often deal with differential equations, but since the computer contains errors, some theoretical basic knowledge is required to judge whether the obtained solution is reliable or not. In this class, you learn ”solving method” of typical ordinary differential equations. It is generally difficult to find all solutions of a differential equation. However, finding a suitable solution, we can often prove that there is no other solution or can obtain the other solutions by using the solution. In particular, concerning the class of linear differential equations, it is known that we get all the solutions as a linear combination of a finite number of fundamental solutions. In order to learn such a fact after this class, I will explain the first step of finding solutions.
Goals and objectives
  1. Can describe solutions of differential equations, and their relationships with family of curves.
  2. Can solve typical 1st order differential equations.
  3. Can solve linear differential equations with constant coefficients.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 5% 5% 10%
2. 45% 15% 60%
3. 30% 30%
Total. 50% 50% -
Evaluation method and criteria
Mid-term exam: 50% Final exam: 50%

Pass when reaching 60% of the whole evaluation, or in other words, reaching the level of understanding and confirming the solutions to given ODEs, solving typical 1st order ODEs of separation-of-variable type and homogeneous type, and solving simple linear ODEs with constant coefficients.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Solutions of differential equations, relationships with family of curves Check out ”differential calculus” in advance. 190minutes
2. 1st order differential equations (separation-of-variable type) Review Session 1 in advance. 190minutes
3. 1st order differential equations (homogeneous type) Review Session 2 in advance. 190minutes
4. 1st order linear differential equations Review Session 3 in advance. 190minutes
5. 1st order complete differential equations Review Session 4 in advance. 190minutes
6. Other differential equations, applications of ODE Review Session 5 in advance. 190minutes
7. Mid-term exam and review Review Sessions 1-6 in advance. 190minutes
8. Linear differential equations and differential operators Check out ”linearlity” in advance. 190minutes
9. Homogeneous linear differential equations with constant coefficients Review Session 8 in advance. 190minutes
10. Inverse differential operators Review Session 9 in advance. 190minutes
11. Linear differential equations with constant coefficients Review Session 10 in advance. 190minutes
12. Solving linear differential equations with constant coefficients by differential operators Review Session 11 in advance. 190minutes
13. Simultaneous differential equations Review Session 12 in advance. 190minutes
14. Final exam and review Review Sessions 1-13 in advance. 190minutes
Total. - - 2660minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in/outside the class.
Textbooks and reference materials
Yano and Ishihara, ”Differential Equations”, Shokabo (in Japanese), ISBN 978-4-7853-1086-8
Prerequisites
Office hours and How to contact professors for questions
  • During class periods, every Monday afternoon (reserve in advance when visiting).
  • The Learning Support Office is open to questions regarding this course.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 5.GENDER EQUALITY
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
  • 13.CLIMATE ACTION
Last modified : Sat Mar 14 14:21:38 JST 2026