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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Miura Tatsuya
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(H119A)
- Group
- -
- Course number
- MTH.C501
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 3Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
This course gives a lecture on the theory of geometric variational problems, with a special emphasis on the theory of elastic curves. This course will be completed with "Advanced topics in Analysis F" in the next quarter.
The aim of this course is to learn some aspects of geometric variational problems through applications to the theory of elastic curves.
Student learning outcomes
・To be familiar with the theory of elastic curves.
・To understand general theory of geometric variational problems.
Keywords
variational analysis, geometric analysis, theory of curves and surfaces, differential equation, elastic curve
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The following topics will be covered: -- Review of Sobolev spaces -- Direct method in calculus of variations -- Euler-Lagrange equation and multiplier method -- Applications to concrete problems including elastic curves -- Classical theory and recent developments on elastic curves | Details will be provided in class. |
Out-of-Class Study Time (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)
None required
Reference books, course materials, etc.
Details will be provided during each class.
Assessment criteria and methods
Attendance and Assignments.
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basics of Lebesgue integral theory, functional analysis, theory of curves and surfaces, and theory of (ordinary) differential equations
