2024 Faculty Courses School of Science Undergraduate major in Mathematics
Differential Equations I
- 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) - 3-4 Wed
- Class
- -
- Course Code
- MTH.C341
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
After introducing some terminology and fundamental notions on differential equations, we explain elementary method for explicit solutions, general method for solving constant coefficient linear differential equations and some analysis on linear differential equations. This course is to be continued to Differential Equations II.
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
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. Students are expected to master method of solving differential equations, and to understand the theory to derive properties of solutions.
Keywords
differential equation, initial value problem, separation of variables, complete differential equation, fundamental solution, Duhamel principle
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | examples of differential equation, solutions of differential equation, initial value problem and boundary value problem | Details will be provided during each class session |
| Class 2 | elementary method, separation of variables, homogeneous case, first order linear differential equation | Details will be provided during each class session |
| Class 3 | complete differential equation, non-normal form, higher order differential equation | Details will be provided during each class session |
| Class 4 | linear ordinary differential equation, exponential function of matrix and constant coefficient system of ordinary differential equations | Details will be provided during each class session |
| Class 5 | variable coefficient system of ordinary differential equations and fundamental solution | Details will be provided during each class session |
| Class 6 | non-homogeneous equation and Duhamel principle | Details will be provided during each class session |
| Class 7 | solution via series expansion | 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.C342 ： Differential Equations II
Prerequisites
Students are expected to have passed Calculus I / Recitation, Calculus II / Recitation, Linear Algebra I / Recitation, Linear Algebra II / Recitation.