2022 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Tatsuya Miura
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue (H119A)
- Class
- -
- Course Code
- MTH.C501
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
・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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
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)
None required
Reference books, course materials, etc.
Details will be provided during each class.
Evaluation methods and criteria
Attendance and Assignments.
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
Prerequisites
Basics of Lebesgue integral theory, functional analysis, theory of curves and surfaces, and theory of (ordinary) differential equations