2024 Faculty Courses School of Science Undergraduate major in Mathematics
Differential Equations II
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Yoshiyuki Kagei
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Tue
- Class
- -
- Course Code
- MTH.C342
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The main topic of this course is nonlinear differential equation. Other topics cover existence and uniqueness of initial value problem, continuous dependence on parameters and theory of finite dimensional dynamical system. This course is a continuation of Differential Equations I.
Differential equations are fundamental notions appearing in all fields of mathematics. Space of solutions have algebraic structure, existence theorems of solutions give various geometric and analytic objects of great interests. This course is an entry to these paths.
Course description and aims
The main topic of this course is a basic theory and its applications of ordinary differential equations of one unknown variable. Ordinary differential equations describe various natural phenomena and physical laws, thus, method of solving equations and its theory are important mathematically as well as for applications. Method of solving ordinary differential equation and theory for analyzing qualitative properties of solutions are to be discussed. Applications to science and engineering will be also discussed.
Keywords
nonlinear ordinary differential equation, existence and uniqueness of solution, stability
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard course lecture.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | nonlinear ordinary differential equation | Details will be provided during each class session |
| Class 2 | existence and uniqueness of solution | Details will be provided during each class session |
| Class 3 | dependence of solution on initial value and parameter | Details will be provided during each class session |
| Class 4 | vector field and its flow | Details will be provided during each class session |
| Class 5 | stability | Details will be provided during each class session |
| Class 6 | phase space | Details will be provided during each class session |
| Class 7 | Hamilton flow, gradient flow | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
not specified
Reference books, course materials, etc.
Eiji Yanagida and Ei Shin-Ichiro, "Theory of ordinary differential equations", Asakura Shoten (Japanese)
Koji Kasahara, "Fundamentals of differential equations", Asakura Shoten (Japanese)
Evaluation methods and criteria
Evaluation based on a final exam. Details will be provided in the class.
Related courses
- MTH.C341 ： Differential Equations I
Prerequisites
Students are expected to have passed Differential Equations I.